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

## Step 1: Finding the Inverse Function<br />### To find the inverse of $f(x) = x + 13$, replace $f(x)$ with $y$, so we have $y = x + 13$. Then, swap $x$ and $y$ to get $x = y + 13$. Finally, solve for $y$: $y = x - 13$. Therefore, $f^{-1}(x) = x - 13$. This inverse function has no restrictions on the domain.<br /><br />## Step 2: Verification of the Inverse<br />### To verify, we need to show that $f(f^{-1}(x)) = x$ and $f^{-1}(f(x)) = x$.<br />First, let's check $f(f^{-1}(x))$:<br />$f(f^{-1}(x)) = f(x - 13) = (x - 13) + 13 = x$.<br /><br />Next, let's check $f^{-1}(f(x))$:<br />$f^{-1}(f(x)) = f^{-1}(x + 13) = (x + 13) - 13 = x$.<br /><br />Both compositions result in $x$, confirming that the inverse function is correct.