Question 1

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

Accepted Answer

A function where no two different elements in the domain map to the same element in the range.

Question 2

Given $$f(x) = 3x - 2$$, what is the inverse function $$f^{-1}(x$$)$$?

Accepted Answer

$$f^{-1}(x$$) = \frac{x-2}{3}$$

Question 3

Which geometric test can be used to determine if a function is one-to-one?

Accepted Answer

Horizontal Line Test

Question 4

If $$f(x) = x^3$, is f$ a one-to-one function? Why?

Accepted Answer

Yes, because no two different numbers have the same cube.

Question 5

Suppose $$f(1) = 5$$, $$f(3) = 7$$, and $$f(8) = -10. $$What is $$f^{-1}(7$$)$$?

Accepted Answer

$$3$$

Question 6

Which property must be satisfied for $$f$$ and $$f^{-1} to be $$true inverses?

Accepted Answer

$$f(f^{-1}(x)) = x$ for every x$ in the domain of f$$^{-1}$$

Question 7

If a pizza costs $$p = 12 + 2n$$ dollars, where $$n is $$the number of toppings, what does the inverse function $$f^{-1}(p$$)$$ represent?

Accepted Answer

The number of toppings for a pizza that costs $$p$$ dollars.

Question 8

Find the inverse of the rational function $$f(x) = \frac{2x+3}{x-1}.$$

Accepted Answer

Question 9

If the graph of $$f is $$reflected over the line $$y = x$$, what does the resulting graph represent?

Accepted Answer

The graph of the inverse function $$f^{-1}(x$$)$$.

Question 10

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

Accepted Answer

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

Question 11

Which of the following is NOT a property of one-to-one functions?

Accepted Answer

A function that fails the horizontal line test is one-to-one.

Question 12

If $$f(x) = x^2$ for x$$ \geq 0$$, what is f$$^{-1}$$(x)$$?

Accepted Answer

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

Question 13

A function $$f is $$defined on domain $$A$$ and range $$B. If$$ $$f is $$one-to-one, what is true about its inverse $$f^{-1}$$?

Accepted Answer

$$f^{-1}$$ maps $$B to$$ $$A$$ and is also one-to-one.

Question 14

If $$f(x) is a $$decreasing function, what can be said about its one-to-one property?

Accepted Answer

It is always one-to-one.

Question 15

If $$f(x) = 12 + 2x$$ models the price of a pizza with $$x$$ toppings, how many toppings does a pizza costing $$22$$ dollars have?

Accepted Answer

$$5$$

Question 16

Which of the following is the correct cancellation property for inverse functions?

Accepted Answer

$$f(f^{-1}(x)) = x$ for every x$ in the domain of f$$^{-1}$$

One-to-One Functions and Their Inverses: College Algebra Study Notes

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