Question

let $f(x) = \sqrt{x}$ and $g(x) = \frac{1}{x + 4}$. find the composition function. $f(g(x)) = $

Explanation:

Step1: Substitute $g(x)$ into $f(x)$

Replace $x$ in $f(x)=\sqrt{x}$ with $g(x)=\frac{1}{x+4}$.
$f(g(x)) = \sqrt{g(x)} = \sqrt{\frac{1}{x+4}}$

Step2: Simplify the radical expression

Use the property $\sqrt{\frac{a}{b}}=\frac{\sqrt{a}}{\sqrt{b}}$ for $a>0, b>0$.
$f(g(x)) = \frac{\sqrt{1}}{\sqrt{x+4}} = \frac{1}{\sqrt{x+4}}$

Answer:

$\frac{1}{\sqrt{x+4}}$ (or equivalently $\sqrt{\frac{1}{x+4}}$)