Algebra Examples

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

Step 1

Set up the composite result function.

$f (g (x))$

Step 2

Evaluate $f (4 x - 5)$ by substituting in the value of $g$ into $f$ .

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

Step 3

Factor $4 x - 5$ out of ${(4 x - 5)}^{2} + 2 (4 x - 5)$ .

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Step 3.1

Factor $4 x - 5$ out of ${(4 x - 5)}^{2}$ .

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

Step 3.2

Factor $4 x - 5$ out of $2 (4 x - 5)$ .

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

Step 3.3

Factor $4 x - 5$ out of $(4 x - 5) (4 x - 5) + (4 x - 5) \cdot 2$ .

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

Step 4

Add $- 5$ and $2$ .

$f (4 x - 5) = \sqrt[3]{(4 x - 5) (4 x - 3)}$