Precalculus Examples

$f (x) = 3 x + 2$ , $g (x) = 2 x - 7$ , $(g \circ f)$

Step 1

Set up the composite result function.

$g (f (x))$

Step 2

Evaluate $g (3 x + 2)$ by substituting in the value of $f$ into $g$ .

$g (3 x + 2) = 2 (3 x + 2) - 7$

Step 3

Simplify each term.

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Step 3.1

Apply the distributive property.

$g (3 x + 2) = 2 (3 x) + 2 \cdot 2 - 7$

Step 3.2

Multiply $3$ by $2$ .

$g (3 x + 2) = 6 x + 2 \cdot 2 - 7$

Step 3.3

Multiply $2$ by $2$ .

$g (3 x + 2) = 6 x + 4 - 7$

Step 4

Subtract $7$ from $4$ .

$g (3 x + 2) = 6 x - 3$