Algebra Examples

$f (x) = 3 x + 5$ , $g (x) = - 2 x - 3$

Step 1

Set up the composite result function.

$f (g (x))$

Step 2

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

$f (- 2 x - 3) = 3 (- 2 x - 3) + 5$

Step 3

Simplify each term.

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Step 3.1

Apply the distributive property.

$f (- 2 x - 3) = 3 (- 2 x) + 3 \cdot - 3 + 5$

Step 3.2

Multiply $- 2$ by $3$ .

$f (- 2 x - 3) = - 6 x + 3 \cdot - 3 + 5$

Step 3.3

Multiply $3$ by $- 3$ .

$f (- 2 x - 3) = - 6 x - 9 + 5$

Step 4

Add $- 9$ and $5$ .

$f (- 2 x - 3) = - 6 x - 4$