Precalculus Examples

$f (x) = 2 x + 3$ $g (x) = 4 x - 2$ Find $((f \circ g)) (x)$

Step 1

Set up the composite result function.

$f (g (x))$

Step 2

Evaluate $f (4 x - 2)$ by substituting in the value of $g$ into $f$ .

$f (4 x - 2) = 2 (4 x - 2) + 3$

Step 3

Simplify each term.

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Step 3.1

Apply the distributive property.

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

Step 3.2

Multiply $4$ by $2$ .

$f (4 x - 2) = 8 x + 2 \cdot - 2 + 3$

Step 3.3

Multiply $2$ by $- 2$ .

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

Step 4

Add $- 4$ and $3$ .

$f (4 x - 2) = 8 x - 1$