Find g(f(x)) f(x) = square root of x+4 , g(x)=x^2

$f (x) = \sqrt{x + 4}$ , $g (x) = x^{2}$

Set up the composite result function.

$g (f (x))$

Evaluate $g (\sqrt{x + 4})$ by substituting in the value of $f$ into $g$ .

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

Rewrite ${\sqrt{x + 4}}^{2}$ as $x + 4$ .

Use $\sqrt[n]{a^{x}} = a^{\frac{x}{n}}$ to rewrite $\sqrt{x + 4}$ as ${(x + 4)}^{\frac{1}{2}}$ .

$g (\sqrt{x + 4}) = {({(x + 4)}^{\frac{1}{2}})}^{2}$

Apply the power rule and multiply exponents, ${(a^{m})}^{n} = a^{m n}$ .

$g (\sqrt{x + 4}) = {(x + 4)}^{\frac{1}{2} \cdot 2}$

Combine $\frac{1}{2}$ and $2$ .

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

Cancel the common factor of $2$ .

Cancel the common factor.

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

Rewrite the expression.

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

Simplify.

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