Find g(f(x)) f(x)=x^2+9 , g(x) = square root of x-9

$f (x) = x^{2} + 9$ , $g (x) = \sqrt{x - 9}$

Set up the composite result function.

$g (f (x))$

Evaluate $g (f (x))$ by substituting in the value of $f$ into $g$ .

$g (x^{2} + 9) = \sqrt{(x^{2} + 9) - 9}$

Subtract $9$ from $9$ .

$g (x^{2} + 9) = \sqrt{x^{2} + 0}$

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

$g (x^{2} + 9) = \sqrt{x^{2}}$

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

$g (x^{2} + 9) = x$

Find g(f(x)) f(x)=x^2+9 , g(x) = square root of x-9