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

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

Step 1

Set up the composite result function.

$g (f (x))$

Step 2

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

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

Step 3

Subtract $4$ from $4$ .

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

Step 4

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

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

Step 5

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

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