Precalculus Examples

$g (x) = 3 x - 1$ , $h (x) = - 3 x^{3} - 3 x^{2}$

Step 1

Set up the composite result function.

$g (h (x))$

Step 2

Evaluate $g (- 3 x^{3} - 3 x^{2})$ by substituting in the value of $h$ into $g$ .

$g (- 3 x^{3} - 3 x^{2}) = 3 (- 3 x^{3} - 3 x^{2}) - 1$

Step 3

Simplify each term.

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Step 3.1

Apply the distributive property.

$g (- 3 x^{3} - 3 x^{2}) = 3 (- 3 x^{3}) + 3 (- 3 x^{2}) - 1$

Step 3.2

Multiply $- 3$ by $3$ .

$g (- 3 x^{3} - 3 x^{2}) = - 9 x^{3} + 3 (- 3 x^{2}) - 1$

Step 3.3

Multiply $- 3$ by $3$ .

$g (- 3 x^{3} - 3 x^{2}) = - 9 x^{3} - 9 x^{2} - 1$