Precalculus Examples

$f (x) = 3 x^{2} + 4 x - 3$ $g (x) = - 2 x - 5$ Find: $g (f (x))$

Step 1

Set up the composite result function.

$g (f (x))$

Step 2

Evaluate $g (3 x^{2} + 4 x - 3)$ by substituting in the value of $f$ into $g$ .

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

Step 3

Simplify each term.

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Step 3.1

Apply the distributive property.

$g (3 x^{2} + 4 x - 3) = - 2 (3 x^{2}) - 2 (4 x) - 2 \cdot - 3 - 5$

Step 3.2

Simplify.

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Step 3.2.1

Multiply $3$ by $- 2$ .

$g (3 x^{2} + 4 x - 3) = - 6 x^{2} - 2 (4 x) - 2 \cdot - 3 - 5$

Step 3.2.2

Multiply $4$ by $- 2$ .

$g (3 x^{2} + 4 x - 3) = - 6 x^{2} - 8 x - 2 \cdot - 3 - 5$

Step 3.2.3

Multiply $- 2$ by $- 3$ .

$g (3 x^{2} + 4 x - 3) = - 6 x^{2} - 8 x + 6 - 5$

Step 4

Subtract $5$ from $6$ .

$g (3 x^{2} + 4 x - 3) = - 6 x^{2} - 8 x + 1$