Find f(g(x)) f(x) = square root of x+5 , g(x)=x^2-5

$f (x) = \sqrt{x + 5}$ , $g (x) = x^{2} - 5$

Step 1

Set up the composite result function.

$f (g (x))$

Step 2

Evaluate $f (x^{2} - 5)$ by substituting in the value of $g$ into $f$ .

$f (x^{2} - 5) = \sqrt{(x^{2} - 5) + 5}$

Step 3

Add $- 5$ and $5$ .

$f (x^{2} - 5) = \sqrt{x^{2} + 0}$

Step 4

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

$f (x^{2} - 5) = \sqrt{x^{2}}$

Step 5

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

$f (x^{2} - 5) = x$