Question

the function \\(f(x) = \frac{10}{x}\\) is one-to-one.

a. find an equation for \\(f^{-1}(x)\\), the inverse function.
b. verify that your equation is correct by showing that \\(f(f^{-1}(x)) = x\\) and \\(f^{-1}(f(x)) = x\\).

a. select the correct choice below and, if necessary, fill in the answer box to complete your choice.
(simplify your answer. use integers or fractions for any numbers in the expression.)

a. \\(f^{-1}(x) = \square\\), for \\(x \le \square\\)
b. \\(f^{-1}(x) = \square\\), for all \\(x\\)
c. \\(f^{-1}(x) = \square\\), for \\(x \
e \square\\)
d. \\(f^{-1}(x) = \square\\), for \\(x \ge \square\\)

Explanation:

Find the inverse function

Using the Inverse Functions knowledge point

$$
LATEXBLOCK0
$$

Determine the domain restriction

Using the Domain of Rational Functions knowledge point

$$
LATEXBLOCK1
$$

Match with the multiple-choice options

Using the Inverse Functions knowledge point

$$
LATEXBLOCK2
$$

This matches option C.

Answer:

• A. \(f^{-1}(x) = \text{blank}\), for \(x \le \text{blank}\)
• B. \(f^{-1}(x) = \text{blank}\), for all \(x\)
• **C. \(f^{-1}(x) = \frac{10}{x}\), for \(x

e 0\) (Correct answer)**

• D. \(f^{-1}(x) = \text{blank}\), for \(x \ge \text{blank}\)