This question tests your ability to read values of an inverse function from a table or graph using the fundamental property that inverses swap inputs and outputs. If f has a table or graph showing its (x, y) pairs, then f⁻¹ has the same pairs but swapped: every (x, y) on f becomes (y, x) on f⁻¹. So to find f⁻¹(a), you don't need the inverse's table or graph—just find where y = a in f's representation and read the corresponding x-value. That x is your answer! For example, if f's table shows x = 3 gives y = 7, then f⁻¹(7) = 3. The inverse reverses the input-output relationship. To find $f^{-1}$(13), look in the f(x) column for the value 13; you'll see it's paired with x=7 in the table. Choice C correctly finds f⁻¹(13) = 7 by reading from the table properly. It's easy to misread and pick a nearby value like 6 or 9, but always verify the exact match in the output column— excellent work persisting through this! Table reading strategy for f⁻¹(a): (1) Look in the f(x) column (the outputs) for the value a, (2) When you find a, look at the x-value in that same row, (3) That x-value is f⁻¹(a). Example: table shows x: 1, 2, 3, 4 and f(x): 5, 9, 13, 17. To find f⁻¹(13), scan the f(x) column for 13 (found in row 3), read x from that row (x = 3), so f⁻¹(13) = 3. The swap happens automatically when you read this way!

This question tests your ability to read values of an inverse function from a table or graph using the fundamental property that inverses swap inputs and outputs. If f has a table or graph showing its (x, y) pairs, then f⁻¹ has the same pairs but swapped: every (x, y) on f becomes (y, x) on f⁻¹. So to find f⁻¹(a), you don't need the inverse's table or graph—just find where y = a in f's representation and read the corresponding x-value. That x is your answer! For example, if f's table shows x = 3 gives y = 7, then f⁻¹(7) = 3. The inverse reverses the input-output relationship. To find $f^{-1}$(0), look in the f(x) column for the value 0; you'll see it's paired with x=2 in the table. Choice B correctly finds f⁻¹(0) = 2 by reading from the table properly. One might accidentally pick 0 or a negative, but recall we're reversing: find input for that output— you're making fantastic progress! Table reading strategy for f⁻¹(a): (1) Look in the f(x) column (the outputs) for the value a, (2) When you find a, look at the x-value in that same row, (3) That x-value is f⁻¹(a). Example: table shows x: 1, 2, 3, 4 and f(x): 5, 9, 13, 17. To find f⁻¹(13), scan the f(x) column for 13 (found in row 3), read x from that row (x = 3), so f⁻¹(13) = 3. The swap happens automatically when you read this way!

This question tests your ability to read values of an inverse function from a table or graph using the fundamental property that inverses swap inputs and outputs. If f has a table or graph showing its (x, y) pairs, then f⁻¹ has the same pairs but swapped: every (x, y) on f becomes (y, x) on f⁻¹. So to find f⁻¹(a), you don't need the inverse's table or graph—just find where y = a in f's representation and read the corresponding x-value. That x is your answer! For example, if f's table shows x = 3 gives y = 7, then f⁻¹(7) = 3. The inverse reverses the input-output relationship. To find $f^{-1}$(2), look in the f(x) column for the value 2; you'll see it's paired with x=1 in the table. Choice C correctly finds f⁻¹(2) = 1 by reading from the table properly. Some students might mistakenly pick 2 itself or confuse with another row, but always focus on locating the output first and grabbing the input— you're doing great, keep going! Table reading strategy for f⁻¹(a): (1) Look in the f(x) column (the outputs) for the value a, (2) When you find a, look at the x-value in that same row, (3) That x-value is f⁻¹(a). Example: table shows x: 1, 2, 3, 4 and f(x): 5, 9, 13, 17. To find f⁻¹(13), scan the f(x) column for 13 (found in row 3), read x from that row (x = 3), so f⁻¹(13) = 3. The swap happens automatically when you read this way!

This question tests your ability to read values of an inverse function from a table or graph using the fundamental property that inverses swap inputs and outputs. If f has a table or graph showing its (x, y) pairs, then f⁻¹ has the same pairs but swapped: every (x, y) on f becomes (y, x) on f⁻¹. So to find f⁻¹(a), you don't need the inverse's table or graph—just find where y = a in f's representation and read the corresponding x-value. That x is your answer! The inverse reverses the input-output relationship. To find f⁻¹(-2), I need to locate -2 in the f(x) column and read the corresponding x-value. Looking at the table, when x = 0, f(x) = -2. Therefore, f⁻¹(-2) = 0. Choice A correctly finds f⁻¹(-2) = 0 by identifying that f(0) = -2 in the table. Choice B incorrectly suggests f⁻¹(-2) = -2, which is the common mistake of thinking a function's inverse at a point equals that point—but this would only be true if the point lies on the line y = x. Table reading strategy for f⁻¹(a): (1) Look in the f(x) column (the outputs) for the value a, (2) When you find a, look at the x-value in that same row, (3) That x-value is f⁻¹(a). In this case, -2 appears in the f(x) column when x = 0, so f⁻¹(-2) = 0.

This question tests your ability to read values of an inverse function from a table or graph using the fundamental property that inverses swap inputs and outputs. If f has a table or graph showing its (x, y) pairs, then f⁻¹ has the same pairs but swapped: every (x, y) on f becomes (y, x) on f⁻¹. So to find f⁻¹(a), you don't need the inverse's table or graph—just find where y = a in f's representation and read the corresponding x-value. That x is your answer! For example, if f's table shows x = 3 gives y = 7, then f⁻¹(7) = 3. The inverse reverses the input-output relationship. Looking for f⁻¹(12), I scan the f(x) column for the value 12: f(0) = 1, f(3) = 6, f(5) = 10, f(6) = 12, f(8) = 16. Found it! When x = 6, f(x) = 12. Therefore, f⁻¹(12) = 6. Choice C correctly finds f⁻¹(12) = 6 by locating the row where f(x) = 12 and reading the corresponding x-value. Choice A incorrectly assumes f⁻¹(12) = 12, which would require f(12) = 12, but 12 isn't even an input in the table. Table reading strategy for f⁻¹(a): (1) Look in the f(x) column (the outputs) for the value a, (2) When you find a, look at the x-value in that same row, (3) That x-value is f⁻¹(a). The process naturally reverses the function's action!

This question tests your ability to read values of an inverse function from a table or graph using the fundamental property that inverses swap inputs and outputs. If f has a table or graph showing its (x, y) pairs, then f⁻¹ has the same pairs but swapped: every (x, y) on f becomes (y, x) on f⁻¹. So to find f⁻¹(a), you don't need the inverse's table or graph—just find where y = a in f's representation and read the corresponding x-value. That x is your answer! For example, if f's table shows x = 3 gives y = 7, then f⁻¹(7) = 3. The inverse reverses the input-output relationship. To evaluate f⁻¹(21), I scan the f(x) column for 21: f(2) = 9, f(4) = 13, f(6) = 17, f(8) = 21, f(10) = 25. Found it! When x = 8, f(x) = 21. Therefore, f⁻¹(21) = 8. Choice C correctly finds f⁻¹(21) = 8 by locating where f(x) = 21 in the table. Choice A incorrectly assumes f⁻¹(21) = 21, which would require f(21) = 21, but 21 isn't even an input value in the table. Table reading strategy for f⁻¹(a): (1) Look in the f(x) column (the outputs) for the value a, (2) When you find a, look at the x-value in that same row, (3) That x-value is f⁻¹(a). The swap happens automatically when you read this way!

This question tests your ability to read values of an inverse function from a table or graph using the fundamental property that inverses swap inputs and outputs. If f has a table or graph showing its (x, y) pairs, then f⁻¹ has the same pairs but swapped: every (x, y) on f becomes (y, x) on f⁻¹. So to find f⁻¹(a), you don't need the inverse's table or graph—just find where y = a in f's representation and read the corresponding x-value. That x is your answer! For example, if f's table shows x = 3 gives y = 7, then f⁻¹(7) = 3. The inverse reverses the input-output relationship. To find f⁻¹(-4), I need to locate -4 in the f(x) column. Scanning down: f(-3) = 5, f(-1) = 1, f(0) = -2, f(2) = -4, f(4) = -7. I found it! When x = 2, f(x) = -4. Therefore, f⁻¹(-4) = 2. Choice A correctly finds f⁻¹(-4) = 2 by identifying that f(2) = -4 in the table. Choice B incorrectly assumes f⁻¹(-4) = -4, missing the fundamental swap property of inverses. Table reading strategy for f⁻¹(a): (1) Look in the f(x) column (the outputs) for the value a, (2) When you find a, look at the x-value in that same row, (3) That x-value is f⁻¹(a). Remember: you're working backwards from output to input!

This question tests your ability to read values of an inverse function from a table or graph using the fundamental property that inverses swap inputs and outputs. If f has a table or graph showing its (x, y) pairs, then f⁻¹ has the same pairs but swapped: every (x, y) on f becomes (y, x) on f⁻¹. So to find f⁻¹(a), you don't need the inverse's table or graph—just find where y = a in f's representation and read the corresponding x-value. That x is your answer! For example, if f's table shows x = 3 gives y = 7, then f⁻¹(7) = 3. The inverse reverses the input-output relationship. Looking for f⁻¹(14), I scan the f(x) column and find f(4) = 14. This means when x = 4, the output is 14, so f⁻¹(14) = 4. Choice B correctly finds f⁻¹(14) = 4 by reading from the table that f(4) = 14 and applying the swap principle. Choice D incorrectly reads 20 from the table, which is actually f(5), not related to finding f⁻¹(14). Table reading strategy for f⁻¹(a): (1) Look in the f(x) column (the outputs) for the value a, (2) When you find a, look at the x-value in that same row, (3) That x-value is f⁻¹(a). Remember, you're working backwards—from output to input—which is exactly what an inverse function does!

This question tests your ability to read values of an inverse function from a table or graph using the fundamental property that inverses swap inputs and outputs. If f has a table or graph showing its (x, y) pairs, then f⁻¹ has the same pairs but swapped: every (x, y) on f becomes (y, x) on f⁻¹. So to find f⁻¹(a), you don't need the inverse's table or graph—just find where y = a in f's representation and read the corresponding x-value. That x is your answer! For example, if f's table shows x = 3 gives y = 7, then f⁻¹(7) = 3. The inverse reverses the input-output relationship. To find f⁻¹(-4), I scan the f(x) column for -4. I see that f(3) = -4, which means when x = 3, the output is -4. Therefore, f⁻¹(-4) = 3. Choice A correctly finds f⁻¹(-4) = 3 by recognizing that since f(3) = -4, the inverse must map -4 back to 3. Choice B incorrectly assumes f⁻¹(-4) = -4, which would mean -4 is a fixed point, but the table shows f(-4) is not even defined. Table reading strategy for f⁻¹(a): (1) Look in the f(x) column (the outputs) for the value a, (2) When you find a, look at the x-value in that same row, (3) That x-value is f⁻¹(a). The problem even gives us a helpful reminder: if f(3) = -4, then f⁻¹(-4) = 3, which directly confirms our answer!