Algebra Examples

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

Step 1

Set up the composite result function.

$g (f (x))$

Step 2

Evaluate $g (3 x + 5)$ by substituting in the value of $f$ into $g$ .

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

Step 3

Simplify each term.

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Step 3.1

Apply the distributive property.

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

Step 3.2

Multiply $3$ by $- 2$ .

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

Step 3.3

Multiply $- 2$ by $5$ .

$g (3 x + 5) = - 6 x - 10 - 3$

Step 4

Subtract $3$ from $- 10$ .

$g (3 x + 5) = - 6 x - 13$