Let and . What is ?
Opening subject page...
Loading your content
Algebra Quiz
Practice Compose Two Functions in Algebra with focused quiz questions that help you check what you know, review explanations, and build confidence with test-style prompts.
Question 1 / 20
0 of 20 answered
Let f(x)=2x and g(x)=x2+1. What is f(g(3))?
This quiz focuses on Compose Two Functions, giving you a quick way to practice the rules, question types, and explanations that matter most for Algebra.
Try each quiz question before looking at the correct answer. Use the explanations to review missed ideas, then come back to similar questions until the pattern feels familiar.
Let f(x)=2x and g(x)=x2+1. What is f(g(3))?
Explanation: This question tests your understanding of function composition—taking the output of one function and using it as the input for another function. To evaluate a composition at a specific number like f(g(3)): Step 1 - find g(3) by substituting 3 into g; Step 2 - take that answer and substitute it into f. If g(3) = 10, then you need f(10). It's like a relay race where g passes its output to f! To find f(g(3)), we work inside-out: First, g(3) = 3² + 1 = 9 + 1 = 10. Now we take this result and plug it into f: f(10) = 2 * 10 = 20. So f(g(3)) = 20. Two separate evaluations, one after the other! Choice A correctly evaluates the composition by working inside-out, giving 20. Choice D has the right process but makes an arithmetic error by doing 2(3²) + 1 instead of 2(3² + 1), leading to 19. When composing functions, there are multiple steps where calculation errors can creep in—always double-check each substitution and simplification! For evaluating at a specific number: do it in TWO separate steps: Step 1: Find g(input) = some number. Step 2: Find f(that number) = final answer. Write down the intermediate answer from Step 1 before moving to Step 2—this prevents mistakes and makes checking easier!
A factory’s total cost C(w) (in dollars) depends on the number of widgets w produced: C(w)=50+8w. The number of widgets produced after d days is w(d)=12d. What does the composition C(w(d)) represent?
Explanation: This question tests your understanding of function composition—taking the output of one function and using it as the input for another function. Function composition f(g(x)) means 'f of g of x': first evaluate g(x), then take that result and plug it into f. Think of it like a two-step process or a chain: x goes into g, g(x) comes out, that goes into f, and f(g(x)) comes out. The inner function (g) is evaluated first, then the outer function (f) is applied to that result. In the context, w(d) gives the number of widgets after d days, and C(w) gives the total cost for w widgets. The composition C(w(d)) means first find widgets after d days, then find the cost for that many widgets. This represents the total cost after d days of production. For example, if w converts days to widgets and C converts widgets to dollars, then C(w(d)) converts days to dollars in one combined operation! Choice C correctly describes the composition by identifying it as the total cost after d days. Choice A reverses the order, describing something like the inverse or a different composition. Remember: f(g(x)) means g is the inner function (evaluated first) and f is the outer function (applied second). The function name closest to x is evaluated first! Quick check to see if you have composition vs. addition: composition has one function INSIDE another (literally nested), while addition has functions side by side with a + between them. f(g(x)) = nested = composition. f(x) + g(x) = side by side = addition. The notation tells you which operation to use!
Given f(x)=x+4 and g(x)=3x−1, compute (f∘g)(5).
Explanation: This question tests your understanding of function composition—taking the output of one function and using it as the input for another function. To evaluate a composition at a specific number like f(g(3)): Step 1 - find g(3) by substituting 3 into g; Step 2 - take that answer and substitute it into f—if g(3) = 7, then you need f(7)—it's like a relay race where g passes its output to f! To find (f ∘ g)(5) where f(x) = √(x + 4) and g(x) = 3x - 1, we work inside-out: First, g(5) = 3(5) - 1 = 15 - 1 = 14; now we take this result and plug it into f: f(14) = √(14 + 4) = √18—so (f ∘ g)(5) = √18. Choice A correctly evaluates the composition by working inside-out, giving √18. Choice B only evaluates the inner function g(5) = 14 but forgets the second step of plugging that into f, or perhaps miscalculates √(14 + 4) as √(14 + 1)—you're not done until you've applied both functions in order! For evaluating at a specific number: do it in TWO separate steps: Step 1: Find g(input) = some number; Step 2: Find f(that number) = final answer—write down the intermediate answer from Step 1 before moving to Step 2—this prevents mistakes and makes checking easier! The golden rule for composition f(g(x)): work INSIDE OUT, just like nested parentheses—the function closest to x (g in this case) gets evaluated first, then its output becomes the input for the next function (f).
Given f(x)=3x+2 and g(x)=x−4, find both f(g(x)) and g(f(x)).
Explanation: This question tests your understanding of function composition—taking the output of one function and using it as the input for another function. Order matters in composition: f(g(x)) is NOT the same as g(f(x)) in general! If f(x) = 3x + 2 and g(x) = x - 4, then f(g(x)) means 'apply g first, then f,' while g(f(x)) means 'apply f first, then g.' Different order, different result! Let's find both directions: For f(g(x)), inner function g gives x - 4, and plugging into f gives f(x - 4) = 3(x - 4) + 2 = 3x - 12 + 2 = 3x - 10. For g(f(x)), inner function f gives 3x + 2, and plugging into g gives g(3x + 2) = (3x + 2) - 4 = 3x - 2. Notice how 3x - 10 ≠ 3x - 2—the order changes everything! Choice A correctly computes both compositions: f(g(x)) = 3x - 10 and g(f(x)) = 3x - 2. Choice B reverses the answers, mixing up which composition gives which result. Remember: the function name closest to x is evaluated first! To remember that order matters: think of real-world sequences. 'Put on socks then shoes' is different from 'put on shoes then socks'! Similarly, 'subtract 4 then triple and add 2' gives a different result than 'triple and add 2 then subtract 4.'
If f(x)=x2 and g(x)=2x−1, what is f(g(x))?
Explanation: This question tests your understanding of function composition—taking the output of one function and using it as the input for another function. Function composition f(g(x)) means 'f of g of x': first evaluate g(x), then take that result and plug it into f. Think of it like a two-step process or a chain: x goes into g, g(x) comes out, that goes into f, and f(g(x)) comes out. The inner function (g) is evaluated first, then the outer function (f) is applied to that result. To find f(g(x)) where f(x) = x² and g(x) = 2x - 1, we substitute the entire expression for g(x) into f: f(g(x)) = f(2x - 1) = (2x - 1)². Every place you see x in f, you replace it with 2x - 1—the whole thing, not just x! Choice B correctly composes the functions by properly substituting g into f, giving (2x - 1)². Choice A makes a substitution error: when replacing x with 2x - 1 in f(x) = x², we need to substitute the ENTIRE expression for g(x), including handling it as a grouped quantity. We get (2x - 1)², not 4x² - 1! To compose functions into a formula: (1) Write down the inner function's expression g(x) = 2x - 1, (2) In the outer function f(x) = x², everywhere you see x, replace it with (2x - 1)—treat it as a single chunk, use parentheses!, (3) The result is (2x - 1)², which we could expand to 4x² - 4x + 1 if needed.
Use the table to evaluate f(g(2)).
Table for g:
Table for f:
Explanation: This question tests your understanding of function composition—taking the output of one function and using it as the input for another function. To evaluate a composition at a specific number like f(g(2)): Step 1 - find g(2) by looking it up in the table; Step 2 - take that answer and substitute it into f. If g(2) = 5, then you need f(5). It's like a relay race where g passes its output to f! To find f(g(2)), we work inside-out: First, from the table, g(2) = 5. Now we take this result and look up f(5) in the table: f(5) = 12. So f(g(2)) = 12. Two separate evaluations, one after the other! Choice B correctly evaluates the composition by working inside-out using the table values, giving 12. Choice A only evaluates the inner function g(2) = 5 but forgets the second step of plugging that into f. You're not done until you've applied both functions in order! For evaluating at a specific number using tables: do it in TWO separate steps: Step 1: Find g(input) = 5 from the table. Step 2: Find f(5) = 12 from the table. Write down the intermediate answer from Step 1 before moving to Step 2—this prevents mistakes and makes checking easier! When working with tables, the process is the same as with formulas: evaluate the inner function first, then use that result as the input for the outer function.
If f(x)=4−x and g(x)=x2, what is g(f(x))?
Explanation: This question tests your understanding of function composition—taking the output of one function and using it as the input for another function. The notation g(f(x)) tells you the order: work from the inside out, with f as the inner function and g as the outer function. If f(x) = 4 - x and g(x) = x², then g(f(x)) means 'plug 4 - x into g,' giving g(4 - x) = (4 - x)². You're replacing every x in g with the entire expression for f(x)! To find g(f(x)) where g(x) = x² and f(x) = 4 - x, we substitute the entire expression for f(x) into g: g(f(x)) = g(4 - x) = (4 - x)². Every place you see x in g, you replace it with 4 - x—the whole thing, treated as a single unit! Choice B correctly composes the functions by properly substituting f into g, giving (4 - x)². Choice A shows 16 - x², which might come from incorrectly thinking (4 - x)² = 4² - x² = 16 - x². Remember: (a - b)² ≠ a² - b²! We need to use the formula (a - b)² = a² - 2ab + b². To compose functions into a formula: (1) Write down the inner function's expression f(x) = 4 - x, (2) In the outer function g(x) = x², everywhere you see x, replace it with (4 - x)—use parentheses to treat it as one chunk!, (3) The result is (4 - x)², which equals 16 - 8x + x² when expanded.
Given f(x)=x and g(x)=x+7, evaluate f(g(9)).
Explanation: This question tests your understanding of function composition—taking the output of one function and using it as the input for another function. To evaluate a composition at a specific number like f(g(9)): Step 1 - find g(9) by substituting 9 into g; Step 2 - take that answer and substitute it into f. If g(9) gives us some value, then we need f(that value). It's like a relay race where g passes its output to f! To find f(g(9)) where f(x) = √x and g(x) = x + 7, we work inside-out: First, g(9) = 9 + 7 = 16. Now we take this result and plug it into f: f(16) = √16 = 4. So f(g(9)) = 4. Two separate evaluations, one after the other! Choice A correctly evaluates the composition by working inside-out, giving 4. Choice B shows √16, which only completes the first step g(9) = 16 but forgets the second step of plugging that into f. You're not done until you've applied both functions in order! The golden rule for composition f(g(x)): work INSIDE OUT, just like nested parentheses. The function closest to x (g in this case) gets evaluated first, then its output becomes the input for the next function (f). For evaluating at a specific number: do it in TWO separate steps: Step 1: Find g(9) = 16. Step 2: Find f(16) = √16 = 4. Write down the intermediate answer from Step 1 before moving to Step 2—this prevents mistakes and makes checking easier!
Let f(x)=x2+2 and g(x)=x−3. Evaluate f(g(0)).
Explanation: This question tests your understanding of function composition—taking the output of one function and using it as the input for another function. To evaluate a composition at a specific number like f(g(0)): Step 1 - find g(0) by substituting 0 into g; Step 2 - take that answer and substitute it into f. If g(0) = -3, then you need f(-3). It's like a relay race where g passes its output to f! To find f(g(0)), we work inside-out: First, g(0) = 0 - 3 = -3. Now we take this result and plug it into f: f(-3) = (-3)² + 2 = 9 + 2 = 11. So f(g(0)) = 11. Two separate evaluations, one after the other! Choice A correctly evaluates the composition by working inside-out, giving 11. Choice B only evaluates the inner function g(0) = -3 but forgets the second step of plugging that into f. You're not done until you've applied both functions in order! For evaluating at a specific number: do it in TWO separate steps: Step 1: Find g(0) = -3. Step 2: Find f(-3) = 11. Write down the intermediate answer from Step 1 before moving to Step 2—this prevents mistakes and makes checking easier! Remember that when squaring a negative number like (-3)², the result is positive: (-3)² = 9, not -9.
If f(x)=2x+3, g(x)=x2, and h(x)=x−1, find f(g(h(x))).
Explanation: This question tests your understanding of function composition—taking the output of one function and using it as the input for another function. The notation f(g(h(x))) can look intimidating, but it's just telling you the order: work from the inside out, just like nested parentheses in arithmetic—first h(x), then g of that, then f of that result—you're replacing step by step! To find f(g(h(x))) where f(x) = 2x + 3, g(x) = x², and h(x) = x - 1, we substitute inward: First, h(x) = x - 1; then g(h(x)) = (x - 1)²; then f(g(h(x))) = 2((x - 1)²) + 3 = 2(x - 1)² + 3—every place you see x in the outer, you build the chain! Choice B correctly composes the functions by properly substituting h into g into f, giving 2(x - 1)² + 3. Choice A makes a substitution error: when replacing with (x - 1) in g(x) = x², it's (x - 1)², not x² - 1, and then applying f correctly—we need to substitute the ENTIRE expression, including handling it as a grouped quantity! The golden rule for composition f(g(h(x))): work INSIDE OUT—the function closest to x (h) gets evaluated first, then g, then f—think: 'h hands to g, g hands to f.' To compose multiple functions: start with the innermost, substitute into the next, and so on, using parentheses to keep track!
If f(x)=2x+1 and g(x)=x−3, which expression equals f(g(x))?
Explanation: This question tests your understanding of function composition—taking the output of one function and using it as the input for another function. Function composition f(g(x)) means 'f of g of x': first evaluate g(x), then take that result and plug it into f. Think of it like a two-step process or a chain: x goes into g, g(x) comes out, that goes into f, and f(g(x)) comes out. To find f(g(x)) where f(x) = 2x + 1 and g(x) = x - 3, we substitute the entire expression for g(x) into f: f(g(x)) = f(x - 3) = 2(x - 3) + 1 = 2x - 6 + 1 = 2x - 5. Every place you see x in f, you replace it with x - 3—the whole thing, not just x! Choice A correctly composes the functions by properly substituting g into f, giving 2x - 5. Choice B has an arithmetic error in the simplification (should be -6 + 1 = -5, not -2), Choice C seems to only use part of f(x), and Choice D shows the unsimplified form but equals 2x - 2, not 2x - 5. The golden rule for composition f(g(x)): work INSIDE OUT, just like nested parentheses. To compose: (1) Write g(x) = x - 3, (2) In f(x) = 2x + 1, replace every x with (x - 3), (3) Simplify: 2(x - 3) + 1 = 2x - 6 + 1 = 2x - 5.
If f(x)=x2 and g(x)=2x−1, which expression represents f(g(x))?
Explanation: This question tests your understanding of function composition—taking the output of one function and using it as the input for another function. The notation f(g(x)) can look intimidating, but it's just telling you the order: work from the inside out, just like nested parentheses in arithmetic. If f(x) = x² and g(x) = 2x - 1, then f(g(x)) means 'plug 2x - 1 into f,' giving f(2x - 1) = (2x - 1)². You're replacing every x in f with the entire expression for g(x)! To find f(g(x)) where f(x) = x² and g(x) = 2x - 1, we substitute the entire expression for g(x) into f: f(g(x)) = f(2x - 1) = (2x - 1)². Every place you see x in f, you replace it with 2x - 1—and since we're squaring, we need parentheses around the whole thing! Choice A correctly composes the functions by properly substituting g into f, giving (2x - 1)². Choices B and C make a substitution error: when replacing x with 2x - 1 in f(x) = x², we need to substitute the ENTIRE expression for g(x), including handling it as a grouped quantity. Since f(x) = x², then f(2x - 1) = (2x - 1)², not 2x² - 1! To compose functions into a formula: (1) Write down the inner function's expression g(x) = 2x - 1, (2) In the outer function f(x) = x², everywhere you see x, replace it with (2x - 1)—treat it as a single chunk, use parentheses!, (3) The result is (2x - 1)², which we could expand if needed.
If f(x)=2x−5 and g(x)=x2+1, what is (f∘g)(x)=f(g(x))?
Explanation: This question tests your understanding of function composition—taking the output of one function and using it as the input for another function. Function composition f(g(x)) means 'f of g of x': first evaluate g(x), then take that result and plug it into f. Think of it like a two-step process or a chain: x goes into g, g(x) comes out, that goes into f, and f(g(x)) comes out. The inner function (g) is evaluated first, then the outer function (f) is applied to that result. To find f(g(x)) where f(x) = 2x - 5 and g(x) = x² + 1, we substitute the entire expression for g(x) into f: f(g(x)) = f(x² + 1) = 2(x² + 1) - 5 = 2x² + 2 - 5 = 2x² - 3. Every place you see x in f, you replace it with (x² + 1)—the whole thing, not just x! Choice B correctly composes the functions by properly substituting g into f, giving 2x² - 3. Choice C multiplies the functions (f(x)·g(x)) instead of composing. Composition is NOT multiplication—it's substitution! f(g(x)) means substitute g(x) into f, not multiply f times g. To compose functions into a formula: (1) Write down the inner function's expression g(x) = x² + 1, (2) In the outer function f(x) = 2x - 5, everywhere you see x, replace it with (x² + 1)—treat it as a single chunk, use parentheses!, (3) Simplify by expanding and combining like terms. The golden rule for composition f(g(x)): work INSIDE OUT, just like nested parentheses.
If h(t)=2t+1 gives the height (in meters) of a drone at time t seconds, and T(y)=y−3 gives the temperature (in °C) at height y meters, what does T(h(t)) represent?
Explanation: This question tests your understanding of function composition—taking the output of one function and using it as the input for another function. Function composition f(g(x)) means 'f of g of x': first evaluate g(x), then take that result and plug it into f. In real-world contexts, this creates a chain of relationships where one quantity depends on another, which depends on a third. In the context, h(t) = 2t + 1 gives the height at time t, and T(y) = y - 3 gives the temperature at height y. The composition T(h(t)) means: first find the height at time t using h(t), then find the temperature at that height using T. This represents the temperature at time t seconds, based on what height the drone is at that time. For example, at t = 5 seconds, the drone is at height h(5) = 11 meters, and the temperature at 11 meters is T(11) = 8°C, so T(h(5)) = 8°C. Choice B correctly describes this as 'The temperature at time t seconds (based on the drone's height then)'. Choice A reverses the meaning, suggesting we input temperature to get height, which would be h(T(y)), not T(h(t)). Remember: the outer function T tells us what the final output represents (temperature), while the inner function h tells us what the input represents (time). To remember composition in context: think of it as a chain of cause and effect. Time determines height (through h), and height determines temperature (through T), so T(h(t)) gives us temperature as a function of time—a two-step relationship where time indirectly affects temperature through the intermediate quantity of height.
Evaluate f(g(−1)) for f(x)=2x−7 and g(x)=x2+4.
Explanation: This question tests your understanding of function composition—taking the output of one function and using it as the input for another function. To evaluate a composition at a specific number like f(g(-1)): Step 1 - find g(-1) by substituting -1 into g; Step 2 - take that answer and substitute it into f. If g(-1) = 5, then you need f(5). It's like a relay race where g passes its output to f! To find f(g(-1)), we work inside-out: First, g(-1) = (-1)² + 4 = 1 + 4 = 5. Now we take this result and plug it into f: f(5) = 2(5) - 7 = 10 - 7 = 3. So f(g(-1)) = 3. Two separate evaluations, one after the other! Choice B correctly evaluates the composition by working inside-out, giving 3. Choice A gives -1, which might result from only evaluating the inner function or confusing the input with the output. For evaluating at a specific number: do it in TWO separate steps: Step 1: Find g(input) = [some number]. Step 2: Find f([that number]) = [final answer]. Write down the intermediate answer from Step 1 before moving to Step 2—this prevents mistakes and makes checking easier!
Let f(x)=x+6 and g(x)=x. Evaluate (f∘g)(25).
Explanation: This question tests your understanding of function composition—taking the output of one function and using it as the input for another function. To evaluate a composition at a specific number like (f∘g)(25): Step 1 - find g(25) by substituting 25 into g; Step 2 - take that answer and substitute it into f. If g(25) = 5, then you need f(5). It's like a relay race where g passes its output to f! To find (f∘g)(25) = f(g(25)), we work inside-out: First, g(25) = √25 = 5. Now we take this result and plug it into f: f(5) = 5 + 6 = 11. So (f∘g)(25) = 11. Two separate evaluations, one after the other! Choice A correctly evaluates the composition by working inside-out, giving 11. Choice D only evaluates the inner function g(25) = √25 = 5 but forgets the second step of plugging that into f. You're not done until you've applied both functions in order! For evaluating at a specific number: do it in TWO separate steps: Step 1: Find g(25) = 5. Step 2: Find f(5) = 11. Write down the intermediate answer from Step 1 before moving to Step 2—this prevents mistakes and makes checking easier! Remember that composition notation (f∘g)(x) is just another way to write f(g(x))—they mean exactly the same thing!
Suppose g(x)=x+4 and f(x)=5−x. Compute (f∘g)(−1).
Explanation: This question tests your understanding of function composition—taking the output of one function and using it as the input for another function. To evaluate a composition at a specific number like f(g(-1)): Step 1 - find g(-1) by substituting -1 into g; Step 2 - take that answer and substitute it into f. If g(-1) = 3, then you need f(3). It's like a relay race where g passes its output to f! To find f(g(-1)), we work inside-out: First, g(-1) = -1 + 4 = 3. Now we take this result and plug it into f: f(3) = 5 - 3 = 2. So f(g(-1)) = 2. Two separate evaluations, one after the other! Choice C correctly evaluates the composition by working inside-out, giving 2. Choice B has the right process but makes an arithmetic error in the second step: f(3) should be 5 - 3 = 2, not something leading to 10. When composing functions, there are multiple steps where calculation errors can creep in—always double-check each substitution and simplification! For evaluating at a specific number: do it in TWO separate steps: Step 1: Find g(input) = some number. Step 2: Find f(that number) = final answer. Write down the intermediate answer from Step 1 before moving to Step 2—this prevents mistakes and makes checking easier!
Let f(x)=x−1 and g(x)=x2+2x. Compute f(g(−1)).
Explanation: This question tests your understanding of function composition—taking the output of one function and using it as the input for another function. To evaluate a composition at a specific number like f(g(-1)): Step 1 - find g(-1) by substituting -1 into g; Step 2 - take that answer and substitute it into f. If g(-1) gives us some value, then we need f(that value). It's like a relay race where g passes its output to f! To find f(g(-1)) where f(x) = x - 1 and g(x) = x² + 2x, we work inside-out: First, g(-1) = (-1)² + 2(-1) = 1 + (-2) = 1 - 2 = -1. Now we take this result and plug it into f: f(-1) = -1 - 1 = -2. So f(g(-1)) = -2. Two separate evaluations, one after the other! Choice A correctly evaluates the composition by working inside-out, giving -2. Choice B shows -1, which only completes the first step g(-1) = -1 but forgets the second step of plugging that into f. You're not done until you've applied both functions in order! For evaluating at a specific number: do it in TWO separate steps: Step 1: Find g(-1) = (-1)² + 2(-1) = 1 - 2 = -1. Step 2: Find f(-1) = -1 - 1 = -2. Write down the intermediate answer from Step 1 before moving to Step 2—this prevents mistakes and makes checking easier!
Suppose f(x)=3x+2 and g(x)=x−5. Which expression represents f(g(x))?
Explanation: This question tests your understanding of function composition—taking the output of one function and using it as the input for another function. The notation f(g(x)) can look intimidating, but it's just telling you the order: work from the inside out, just like nested parentheses in arithmetic. If f(x) = 3x + 2 and g(x) = x - 5, then f(g(x)) means 'plug x - 5 into f,' giving f(x - 5) = 3(x - 5) + 2. You're replacing every x in f with the entire expression for g(x)! To find f(g(x)) where f(x) = 3x + 2 and g(x) = x - 5, we substitute the entire expression for g(x) into f: f(g(x)) = f(x - 5) = 3(x - 5) + 2 = 3x - 15 + 2 = 3x - 13. Every place you see x in f, you replace it with (x - 5)—the whole thing, not just x! Choice B correctly represents the composition by properly substituting g into f, showing 3(x - 5) + 2. Choice A adds the functions (3x + 2) + (x - 5) instead of composing them. These are completely different operations: addition of functions combines outputs, while composition plugs the output of one into the other as input. Watch out for this confusion! Quick check to see if you have composition vs. addition: composition has one function INSIDE another (literally nested), while addition has functions side by side with a + between them. f(g(x)) = nested = composition. f(x) + g(x) = side by side = addition. The notation tells you which operation to use!
For f(x)=x and g(x)=x+15, compute (f∘g)(1).
Explanation: This question tests your understanding of function composition—taking the output of one function and using it as the input for another function. The notation f(g(x)) can look intimidating, but it's just telling you the order: work from the inside out, just like nested parentheses in arithmetic. If f(x)=x and g(x)=x+15, then (f∘g)(1) means we first find g(1), then apply f to that result. To find (f∘g)(1), we work inside-out: First, g(1)=1+15=16. Now we take this result and plug it into f: f(16)=16=4. So (f∘g)(1)=4. Two separate evaluations, one after the other! Choice A correctly evaluates the composition by working inside-out, giving 4. Choice B shows 16 but doesn't complete the evaluation—we need to simplify 16=4. You're not done until you've applied both functions in order and simplified! For evaluating at a specific number: do it in TWO separate steps: Step 1: Find g(input)=16. Step 2: Find f(16)=4. Write down the intermediate answer from Step 1 before moving to Step 2—this prevents mistakes and makes checking easier!