Algebra 2 Practice Test: Inverse Functions
- Inverse Functions
- 10 questions
- 15 minutes
These 10 questions practice finding inverse functions, reading inverses from tables and graphs, and deciding whether an inverse is a function. To find an inverse, swap x and y and solve for y.
Tap an option to mark your answer. You can change your mind, or tap the same option again to leave the question blank. The correct answers and explanations appear when you finish the test.Tap an option to answer; tap it again to leave the question blank.
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Question 1
What is the inverse of f(x) = 3x − 7?
Correct answer: A
Swap: x = 3y − 7, so y = x + 73. The inverse undoes the steps in reverse order: add 7 first, then divide by 3. 13x − 7 is the reciprocal, not the inverse.
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Question 2
What is the inverse of f(x) = 2x + 15?
Correct answer: D
Swap: x = 2y + 15. Then 5x = 2y + 1 and y = 5x − 12.
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Question 3
What is the inverse of f(x) = x3 + 2?
Correct answer: A
Swap: x = y3 + 2, so y3 = x − 2 and y = ∛(x − 2). Taking the cube root before subtracting 2 gives the wrong order of steps.
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Question 4
The function f has an inverse, and f(4) = 11. What is f−1(11)?
Correct answer: B
An inverse swaps inputs and outputs: if f sends 4 to 11, then f−1 sends 11 back to 4. f−1 does not mean 1f.
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Question 5
Which function has an inverse that is also a function?
Correct answer: C
The inverse is a function only if f is one-to-one (passes the horizontal line test). x3 − 1 is always increasing, while the other three give the same output for two different inputs, for example x2 + 1 at x = 1 and x = −1.
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Question 6
How is the graph of y = f−1(x) related to the graph of y = f(x)?
Correct answer: D
Every point (a, b) on the graph of f becomes (b, a) on the graph of the inverse, and swapping coordinates reflects a point over the line y = x.
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Question 7
x 1 2 3 4 f(x) 4 7 10 13 Using the table, what is f−1(7)?
Correct answer: A
Find 7 in the output row: f(2) = 7, so f−1(7) = 2. Reading 7 as an input gives f(7) = 22, which is not what is asked.
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Question 8
What is the inverse of f(x) = x − 3, x ≥ 3?
Correct answer: B
Swap: x = y − 3, so y = x2 + 3. The domain of the inverse is the range of f, which is x ≥ 0, not x ≥ 3.
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Question 9
Which function is the inverse of f(x) = 4x − 8?
Correct answer: C
Check by composition: g(f(x)) = 4x − 84 + 2 = x − 2 + 2 = x. For x4 + 8, g(f(x)) = x + 6, so it is not the inverse.
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Question 10
What is the inverse of f(x) = xx − 2?
Correct answer: B
Swap: x = yy − 2, so xy − 2x = y, y(x − 1) = 2x and y = 2xx − 1. x − 2x is the reciprocal of f, not its inverse.
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