Precalculus Examples

$f (x) = - 2 x - 15$ $g (x) = 2 x^{2} + 3 x + 3$ Find: $((f \circ g)) (x)$

Step 1

Set up the composite result function.

$f (g (x))$

Step 2

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

$f (2 x^{2} + 3 x + 3) = - 2 (2 x^{2} + 3 x + 3) - 15$

Step 3

Simplify each term.

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Step 3.1

Apply the distributive property.

$f (2 x^{2} + 3 x + 3) = - 2 (2 x^{2}) - 2 (3 x) - 2 \cdot 3 - 15$

Step 3.2

Simplify.

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Step 3.2.1

Multiply $2$ by $- 2$ .

$f (2 x^{2} + 3 x + 3) = - 4 x^{2} - 2 (3 x) - 2 \cdot 3 - 15$

Step 3.2.2

Multiply $3$ by $- 2$ .

$f (2 x^{2} + 3 x + 3) = - 4 x^{2} - 6 x - 2 \cdot 3 - 15$

Step 3.2.3

Multiply $- 2$ by $3$ .

$f (2 x^{2} + 3 x + 3) = - 4 x^{2} - 6 x - 6 - 15$

Step 4

Subtract $15$ from $- 6$ .

$f (2 x^{2} + 3 x + 3) = - 4 x^{2} - 6 x - 21$