### Home > A2C > Chapter 11 > Lesson 11.3.1 > Problem 11-132

11-132.

For the function

, complete parts (a) through (d) below. Homework Help ✎ Sketch the graph and the inverse.

Find the equation of the inverse function.

Determine the domain and range of the inverse.

Compute

*f*^{−1}(*f*(5)).

First, graph the function. Then, reflect the graph across

*y* = *x*.

Replace *f*(*x*) with *y*, then switch the variables.

Now solve for *y*.

Do not forget to replace *y* with *f*^{ − 1}(*x*).

*f*^{ −1}(*x*) = (2(*x* + 1))^{2} − 4

See graph in part (a).

*x* ≥ −1, *y* ≥ −4

Substitute 5 for *x* in the function *f*(*x*). Now substitute the answer you found for *f*(*x*) for *x* in the inverse function *f*^{ −1}(*x*).

*f*^{ −1}(*f*(5)) = 5