Question 1

Which of the following statements best describes a one-to-one function?

Accepted Answer

A function where every input corresponds to exactly one output, and every output corresponds to exactly one input.

Question 2

Given the set of ordered pairs $$\{(-3, 5), (-2, 3), (-1, 1), (0, -1), (2, -3)\}$$, is this function one-to-one?

Accepted Answer

Yes, because each input has a unique output and each output is unique.

Question 3

Which function passes the horizontal-line test?

Accepted Answer

$$g(x) = x^5$

Question 4

If a function is increasing on an interval $$I$$, what can be concluded about its one-to-one property on $$I$$?

Accepted Answer

It is one-to-one on $$I.$$

Question 5

What is the inverse function of $$f(x) = 3x - 5$$?

Accepted Answer

$$f^{-1}(x$$) = \frac{1}{3}(x + 5)$$

Question 6

Which of the following is true about the domain and range of a function $$f$$ and its inverse $$f^{-1}$$?

Accepted Answer

Domain of $$f = $$Range of $$f^{-1}$$ and Range of $$f = $$Domain of $$f^{-1}$$

Question 7

The graphs of a one-to-one function $$f$$ and its inverse $$f^{-1}$$ are symmetric with respect to which line?

Accepted Answer

$$y = x$$

Question 8

Given $$f(x) = x^2$ + 1$$ for $$x \geq 0$$, what is the inverse function $$f^{-1}(x$$)$$?

Accepted Answer

$$f^{-1}(x$$) = \sqrt{x - 1}$$

Question 9

Which equation verifies that $$f$$ and $$f^{-1}$$ are inverses?

Accepted Answer

$$f^{-1}(f(x)) = x$ and f(f$$^{-1}$$(x)) = x$$

Question 10

A function $$f(x) is $$defined as $$f(x) = \frac{x + 1}{x - 2}. $$What is the first step to find its inverse?

Accepted Answer

Interchange $$x$$ and $$y in $$the equation.

Question 11

If $$f(x) is $$not one-to-one, which of the following is true?

Accepted Answer

It may fail the horizontal-line test.

Question 12

Which real-world scenario best illustrates a one-to-one function?

Accepted Answer

Assigning each student a unique ID number.

Question 13

Given $$f(x) = 4x - 7$$, what is $$f^{-1}(x$$)$$?

Accepted Answer

$$f^{-1}(x$$) = \frac{x + 7}{4}$$

Question 14

If $$f(x) is $$decreasing on an interval $$I$$, what can be said about its one-to-one property?

Accepted Answer

It is one-to-one on $$I.$$

Question 15

Which of the following is NOT a function?

Accepted Answer

A relation where one input has two outputs.

Question 16

If $$f(x) = x^5$, what is f$$^{-1}$$(x)$$?

Accepted Answer

$$f^{-1}(x$$) = \sqrt[5]{x}$$

Question 17

Which step is necessary to check if your inverse function is correct?

Accepted Answer

Verify that $$f^{-1}(f(x)) = x$ and f(f$$^{-1}$$(x)) = x.$$

Question 18

If $$f(x) = 2x + 1$$, what is $$f^{-1}(x$$)$$?

Accepted Answer

$$f^{-1}(x$$) = \frac{x - 1}{2}$$

Question 19

Which of the following is a multi-step process for finding the inverse of a function defined by an equation?

Accepted Answer

Interchange $$x$$ and $$y$$, solve for $$y$$, and check $$f^{-1}(f(x)) = x$.

One-to-One and Inverse Functions: Precalculus Study Guide

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