The function f(x)=x+13 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 xneq square B. f^-1(x)=square for xleqslant square C. f^-1(x)=square , for all x D. f^-1(x)=square , for xgeqslant square b. Verify that the equation is correct. f(f^-1(x))=f(square ) and f^-1(f(x))=f^-1(square ) Substitute. =square =square Simplify. The equation is square

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Answer 1

### a. C.

, for all x### b.

and

Substitute.

Simplify.

The equation is correct.

Answer 2

## Step 1: Finding the Inverse Function### To find the inverse of

, replace

with

, so we have

. Then, swap

and

to get

. Finally, solve for

:

. Therefore,

. This inverse function has no restrictions on the domain.## Step 2: Verification of the Inverse### To verify, we need to show that

and

.First, let's check

:

.Next, let's check

:

.Both compositions result in

, confirming that the inverse function is correct.

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