### Home > PC > Chapter 1 > Lesson 1.1.3 > Problem1-38

1-38.

$g(x) = \sqrt{2\textit{x}+4}$

$h(x) = \frac{1}{2}\textit{x}^{2} - 2$

$h(4) = \frac{1}{2}4^{2} - 2$

$h(4) = 8 - 2 \Rightarrow 6$

$g(h(4)) = \sqrt{2 \cdot 6 + 4} \Rightarrow 4$

Yes, output and input are the same: -1. Show all of your work!

No, the output is 2 while the input was -2. Show all of your work!

It does not have the same output in part(c) because the inverse of the h function is NOT a function.

There are two outputs for a given input of x. A function can only have one output.