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

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

Set up the composite result function.

$f (g (x))$

Evaluate $f (x^{2} - 4)$ by substituting in the value of $g$ into $f$ .

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

Add $- 4$ and $4$ .

$f (x^{2} - 4) = \sqrt{x^{2} + 0}$

Add $x^{2}$ and $0$ .

$f (x^{2} - 4) = \sqrt{x^{2}}$

Pull terms out from under the radical, assuming positive real numbers.

$f (x^{2} - 4) = x$