Precalculus Examples

$f (x) = 4 x + 3$ , $g (x) = x^{3} - 2$

Step 1

Set up the composite result function.

$f (g (x))$

Step 2

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

$f (x^{3} - 2) = 4 (x^{3} - 2) + 3$

Step 3

Simplify each term.

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Step 3.1

Apply the distributive property.

$f (x^{3} - 2) = 4 x^{3} + 4 \cdot - 2 + 3$

Step 3.2

Multiply $4$ by $- 2$ .

$f (x^{3} - 2) = 4 x^{3} - 8 + 3$

Step 4

Add $- 8$ and $3$ .

$f (x^{3} - 2) = 4 x^{3} - 5$