### Home > A2C > Chapter 7 > Lesson 7.2.3 > Problem 7-132

7-132.

Use

to complete parts (a) through (e) below. Homework Help ✎ What are the domain and range of

*f(x)*?What is the inverse of

*f(x)*? Call it*g(x)*.What are the domain and range of

*g(x)*?Find an expression for

*f(g(x))*.Find an expression for

*g(f(x))*. What do you notice? Why does this happen?

Which values of *x* will cause the square root expression to be undefined?

If *f*(*x*) = *y*, then switch the *x* and the *y* in *f*(*x*). Solve for *y*.

Switch the domain and range of *f*(*x*).

Substitute the equation *g*(*x*) that you found in part (b) for *x* in *f*(*x*).

Simplify.

See part (d). What relationship do *f*(*x*) and *g*(*x*) have with each other? (What is the relationship between two inverses?)