### Home > PC3 > Chapter 4 > Lesson 4.1.1 > Problem4-9

4-9.

Given $f(x)=2x+5$, $g(x)=x^2-1$, and  $h(x)=\sqrt{x+2}$.

1. Evaluate $g(f(h(2)))$.

$h(2)=\sqrt{4}=2$
$g(f(2))=?$

$f(2)=2(2)+5=9$
$g(9)=?$

1. Write an equation for $f(g(h(x)))$.

$f(g(\sqrt{x+2}))$

$g(\sqrt{x+2})=\sqrt{x+2}^2-1=x+1\text{, so}$

$f(x+1)=?$

1. Write an equation for $g(f(x))$.

$g(2x+5)=?$

1. For what value(s) of $x$ will $g(f(x))=48$?

Set your expression from part (c) equal to $48$ and solve for $x$.