Precalculus Examples

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

Step 1

Set up the composite result function.

$f (g (x))$

Step 2

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

$f (x^{2} + 4 x + 2) = 4 (x^{2} + 4 x + 2) + 5$

Step 3

Simplify each term.

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Step 3.1

Apply the distributive property.

$f (x^{2} + 4 x + 2) = 4 x^{2} + 4 (4 x) + 4 \cdot 2 + 5$

Step 3.2

Simplify.

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Step 3.2.1

Multiply $4$ by $4$ .

$f (x^{2} + 4 x + 2) = 4 x^{2} + 16 x + 4 \cdot 2 + 5$

Step 3.2.2

Multiply $4$ by $2$ .

$f (x^{2} + 4 x + 2) = 4 x^{2} + 16 x + 8 + 5$

Step 4

Add $8$ and $5$ .

$f (x^{2} + 4 x + 2) = 4 x^{2} + 16 x + 13$