### Home > CAAC > Chapter 13 > Lesson 13.OF1-S > Problem7-132

7-132.

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.

$\textit{g}(\textit{x})=\frac{(\textit{x}-3)^{2}+1}{2}$

Switch the domain and range of f(x).

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

$f(g(x))=3+\sqrt{2\left(\frac{(x-3)^{2}+1}{2}\right)-1}$

Simplify.

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