Find g(f(x)) f(x) = cube root of x^2+2x , g(x)=4x-5

$f (x) = \sqrt[3]{x^{2} + 2 x}$ , $g (x) = 4 x - 5$

Step 1

Set up the composite result function.

$g (f (x))$

Step 2

Evaluate $g (\sqrt[3]{x^{2} + 2 x})$ by substituting in the value of $f$ into $g$ .

$g (\sqrt[3]{x^{2} + 2 x}) = 4 (\sqrt[3]{x^{2} + 2 x}) - 5$

Step 3

Factor $x$ out of $x^{2} + 2 x$ .

Factor $x$ out of $x^{2}$ .

$g (\sqrt[3]{x^{2} + 2 x}) = 4 \sqrt[3]{x \cdot x + 2 x} - 5$

Factor $x$ out of $2 x$ .

$g (\sqrt[3]{x^{2} + 2 x}) = 4 \sqrt[3]{x \cdot x + x \cdot 2} - 5$

Factor $x$ out of $x \cdot x + x \cdot 2$ .

$g (\sqrt[3]{x^{2} + 2 x}) = 4 \sqrt[3]{x (x + 2)} - 5$