Question

the function \\(f(x) = x + 7\\) 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 fill in the answer box(es) to complete your choice.
(simplify your answer. use integers or fractions for any numbers in the expression.)

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

Explanation:

Find the inverse function

Using the Inverse Functions knowledge point

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Determine the domain of the inverse function

Using the Inverse Functions knowledge point

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Answer:

• (A) \(f^{-1}(x) = \text{for } x \le \)
• (B) \(f^{-1}(x) = x - 7\) for all \(x\) (Correct answer)
• (C) \(f^{-1}(x) = \text{for } x \ge \)
• (D) \(f^{-1}(x) = \text{for } x

e \)