Find g(f(x)) f(x)=x^3-4 , g(x) = cube root of x+4

$f (x) = x^{3} - 4$ , $g (x) = \sqrt[3]{x + 4}$

Step 1

Set up the composite result function.

$g (f (x))$

Step 2

Evaluate $g (x^{3} - 4)$ by substituting in the value of $f$ into $g$ .

$g (x^{3} - 4) = \sqrt[3]{(x^{3} - 4) + 4}$

Step 3

Add $- 4$ and $4$ .

$g (x^{3} - 4) = \sqrt[3]{x^{3} + 0}$

Step 4

Add $x^{3}$ and $0$ .

$g (x^{3} - 4) = \sqrt[3]{x^{3}}$

Step 5

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

$g (x^{3} - 4) = x$