Precalculus Examples

$g (n) = 4 n + 4$ $f (n) = 3 n^{3} - 4$ Find $g (f (n))$

Step 1

Set up the composite result function.

$g (f (n))$

Step 2

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

$g (3 n^{3} - 4) = 4 (3 n^{3} - 4) + 4$

Step 3

Simplify each term.

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Step 3.1

Apply the distributive property.

$g (3 n^{3} - 4) = 4 (3 n^{3}) + 4 \cdot - 4 + 4$

Step 3.2

Multiply $3$ by $4$ .

$g (3 n^{3} - 4) = 12 n^{3} + 4 \cdot - 4 + 4$

Step 3.3

Multiply $4$ by $- 4$ .

$g (3 n^{3} - 4) = 12 n^{3} - 16 + 4$

Step 4

Add $- 16$ and $4$ .

$g (3 n^{3} - 4) = 12 n^{3} - 12$