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) = \square\\), for \\(x \le \square\\)
b. \\(f^{-1}(x) = x - 7\\), for all \\(x\\)
c. \\(f^{-1}(x) = \square\\), for \\(x \ge \square\\)
d. \\(f^{-1}(x) = \square\\), for \\(x \
e \square\\)

b. verify that the equation is correct.
\\(f(f^{-1}(x)) = f(\square) = \square\\) and \\(f^{-1}(f(x)) = f^{-1}(\square) = \square\\)

Explanation:

Find the inverse function

Using the Inverse Functions knowledge point

$$
LATEXBLOCK0
$$

Verify the composition f(f^-1(x))

Using the Function Composition and Inverse Functions knowledge points

$$
LATEXBLOCK1
$$

Verify the composition f^-1(f(x))

Using the Function Composition and Inverse Functions knowledge points

$$
LATEXBLOCK2
$$

Answer:

Question a

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

e \Box\)

Question b

$$
LATEXBLOCK0
$$

and

$$
LATEXBLOCK1
$$