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Example Questions
Example Question #13 : How To Find F(X)
Given the functions f(x) = 2x + 4 and g(x) = 3x – 6, what is f(g(x)) when x = 6?
192
12
28
144
16
28
We need to work from the inside to the outside, so g(6) = 3(6) – 6 = 12.
Then f(g(6)) = 2(12) + 4 = 28.
Example Question #14 : How To Find F(X)
A function f(x) = –1 for all values of x. Another function g(x) = 3x for all values of x. What is g(f(x)) when x = 4?
–3
12
–1
3
–12
–3
We work from the inside out, so we start with the function f(x). f(4) = –1. Then we plug that value into g(x), so g(f(x)) = 3 * (–1) = –3.
Example Question #15 : How To Find F(X)
What is f(–3) if f(x) = x2 + 5?
–14
14
4
–4
15
14
f(–3) = (–3)2 + 5 = 9 + 5 = 14
Example Question #21 : How To Find F(X)
For all values of x, f(x) = 7x2 – 3, and for all values of y, g(y) = 2y + 9. What is g(f(x))?
7y2 – 3
2x + 9
14x2 + 3
14x2 – 3
14y2 + 3
14x2 + 3
The inner function f(x) is like our y-value that we plug into g(y).
g(f(x)) = 2(7x2 – 3) + 9 = 14x2 – 6 + 9 = 14x2 + 3.
Example Question #22 : How To Find F(X)
Find
Simply plug 6 into the equation and don't forget the absolute value at the end.
absolute value = 67
Example Question #41 : Algebraic Functions
An outpost has the supplies to last 2 people for 14 days. How many days will the supplies last for 7 people?
Supplies are used at the rate of .
Since the total amount of supplies is the same in either case, .
Solve for days to find that the supplies will last for 4 days.
Example Question #42 : Algebraic Functions
Worker can make a trinket in 4 hours, Worker
can make a trinket in 2 hours. When they work together, how long will it take them to make a trinket?
The rates are what needs to be added. Rate is
, or one trinket every 4 hours. Rate
is
, one per two hours.
, their combined rate in trinkets per hour.
Now invert the equation to get back to hours per trinket, which is what the question asks for:
Example Question #23 : How To Find F(X)
Quantity A Quantity B
Quantity A is greater
Quantity B is greater
Quantity A and Quantity B are equal
The relationship cannot be determined from the information given.
Quantity A and Quantity B are equal
Since , then we have that
and
.
Thus, the two quantities are equal.
Example Question #44 : Algebraic Functions
If the average of two numbers is and one of the numbers is
, what is the other number, in terms of
and
?
The average is the sum of the terms divided by the number of terms. Here you have and the other number which you can call
. The average of
and
is
. So
Multiply both sides by 2.
Solve for .
Example Question #45 : Algebraic Functions
Alice is twice as old as Tom, but four years ago, she was three years older than Tom is now. How old is Tom now?
The qustion can be broken into two equations with two unknows, Alice age and Tom's age
.
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