Question 1

Which of the following conditions must a function $$f: A 	o B$$ satisfy in order for its inverse $$f^{-1} to $$exist as a function?

Accepted Answer

It must be one-to-one (injective).

Question 2

Given $$f(x) = x^2$ with domain $$\mathbb{R}$$, which of the following statements is true about its inverse?

Accepted Answer

The inverse is not a function unless the domain is restricted.

Question 3

For which of the following values is $$\sin$$^{-1}$$(x)$$ defined?

Accepted Answer

$$x = -1$$

Question 4

Evaluate $$\sin$$^{-1}$$\left(-\frac{1}{2}\right).$$

Accepted Answer

$$-\frac{\pi}{6}$$

Question 5

Which of the following is the correct domain and range for the inverse cosine function $$\cos$$^{-1}$$(x)$$?

Accepted Answer

Domain: $$-1 \leq x \leq 1$$, Range: $$0 \leq y \leq \pi$$

Question 6

Find $$\cos$$^{-1}$$\left(-\frac{1}{2}\right).$$

Accepted Answer

$$\frac{2\pi}{3}$$

Question 7

Evaluate $$	an$$^{-1}$$(-\sqrt{3}).$$

Accepted Answer

$$-\frac{\pi}{3}$$

Question 8

Which of the following is the correct principal value range for $$\sin$$^{-1}$$(x)$$?

Accepted Answer

$$-\frac{\pi}{2} \leq y \leq \frac{\pi}{2}$$

Question 9

If $$\sin$$^{-1}$$(\sin(\frac{5\pi}{8})) is $$evaluated, what is the result?

Accepted Answer

$$\frac{3\pi}{8}$$

Question 10

Which of the following expressions is NOT defined?

Accepted Answer

$$\cos(\cos$$^{-1}$$(2.4))$$

Question 11

Suppose $$f(x) = x^2$ with domain x$$ \geq 0$$. What is f$$^{-1}$$(x)$$?

Accepted Answer

$$\sqrt{x}$$

Question 12

Which of the following is the correct domain and range for the inverse tangent function $$	an$$^{-1}$$(x)$$?

Accepted Answer

Domain: $$-\infty \u003c x \u003c \infty$$, Range: $$-\frac{\pi}{2} \u003c y \u003c \frac{\pi}{2}$$

Question 13

If $$f(x) = x^2$ and f$$^{-1}$$ is defined only for x$$ \geq 0$$, what is the range of f$?

Accepted Answer

$$[0, \infty)$$

Question 14

Which of the following is true about the graph of $$y = \sin$$^{-1}$$(x)$$?

Accepted Answer

It is the reflection of $$y = \sin(x) ($$restricted to $$[-\frac{\pi}{2}, \frac{\pi}{2}]) $$over the line $$y = x.$$

Question 15

Evaluate $$\cos\left[\cos$$^{-1}$$(\pi)\right].$$

Accepted Answer

Not defined

Question 16

Which of the following statements about inverse trigonometric functions is correct?

Accepted Answer

$$\sin$$^{-1}$$(x) is $$defined only for $$-1 \leq x \leq 1.$$

Inverse Functions and Inverse Trigonometric Functions

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