### Home > A2C > Chapter 7 > Lesson 7.2.3 > Problem7-132

7-132.

Use$f ( x ) = 3 + \sqrt { 2 x - 1 }$ to complete parts (a) through (e) below.

1. What are the domain and range of f(x)?

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

2. 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.

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

3. What are the domain and range of g(x)?

Switch the domain and range of f(x).

4. Find an expression for f(g(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.

5. 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?)