Precalculus Examples

$f (x) = - x - 4$ $g (x) = 2 x^{2} + 4 x + 11$ Find: $((f \circ g)) (x)$

Step 1

Set up the composite result function.

$f (g (x))$

Step 2

Evaluate $f (2 x^{2} + 4 x + 11)$ by substituting in the value of $g$ into $f$ .

$f (2 x^{2} + 4 x + 11) = - (2 x^{2} + 4 x + 11) - 4$

Step 3

Simplify each term.

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Step 3.1

Apply the distributive property.

$f (2 x^{2} + 4 x + 11) = - (2 x^{2}) - (4 x) - 1 \cdot 11 - 4$

Step 3.2

Simplify.

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Step 3.2.1

Multiply $2$ by $- 1$ .

$f (2 x^{2} + 4 x + 11) = - 2 x^{2} - (4 x) - 1 \cdot 11 - 4$

Step 3.2.2

Multiply $4$ by $- 1$ .

$f (2 x^{2} + 4 x + 11) = - 2 x^{2} - 4 x - 1 \cdot 11 - 4$

Step 3.2.3

Multiply $- 1$ by $11$ .

$f (2 x^{2} + 4 x + 11) = - 2 x^{2} - 4 x - 11 - 4$

Step 4

Subtract $4$ from $- 11$ .

$f (2 x^{2} + 4 x + 11) = - 2 x^{2} - 4 x - 15$