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

7-132.

Use

What are the domain and range of

*f(x)*?Which values of

*x*will cause the square root expression to be undefined?What is the inverse of

*f(x)*? Call it*g(x)*.If

*f*(*x*) =*y*, then switch the*x*and the*y*in*f*(*x*). Solve for*y*.What are the domain and range of

*g(x)*?Switch the domain and range of

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

*f(g(x))*.Substitute the equation

*g*(*x*) that you found in part (b) for*x*in*f*(*x*).Simplify.

Find an expression for

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

*f*(*x*) and*g*(*x*) have with each other? (What is the relationship between two inverses?)