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

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

Step 1

Set up the composite result function.

$g (f (x))$

Step 2

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

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

Step 3

Add $- 3$ and $3$ .

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

Step 4

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

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

Step 5

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

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