Find f(g(x)) f(x) = square root of x+1 , g(x)=x^2-1

$f (x) = \sqrt{x + 1}$ , $g (x) = x^{2} - 1$

Set up the composite result function.

$f (g (x))$

Evaluate $f (x^{2} - 1)$ by substituting in the value of $g$ into $f$ .

$f (x^{2} - 1) = \sqrt{(x^{2} - 1) + 1}$

Add $- 1$ and $1$ .

$f (x^{2} - 1) = \sqrt{x^{2} + 0}$

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

$f (x^{2} - 1) = \sqrt{x^{2}}$

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

$f (x^{2} - 1) = x$