Precalculus Examples

$f (x) = 3 x^{2}$ , $g (x) = x + 1$ , fog

Set up the composite result function.

$f (g (x))$

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

$3 {(x + 1)}^{2}$

Rewrite ${(x + 1)}^{2}$ as $(x + 1) (x + 1)$ .

$f (x + 1) = 3 ((x + 1) (x + 1))$

Expand $(x + 1) (x + 1)$ using the FOIL Method.

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Apply the distributive property.

$f (x + 1) = 3 (x (x + 1) + 1 (x + 1))$

Apply the distributive property.

$f (x + 1) = 3 (x x + x \cdot 1 + 1 (x + 1))$

Apply the distributive property.

$f (x + 1) = 3 (x x + x \cdot 1 + (1 x + 1 \cdot 1))$

Remove parentheses.

$f (x + 1) = 3 (x x + x \cdot 1 + 1 x + 1 \cdot 1)$

Simplify and combine like terms.

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Simplify each term.

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Simplify $x^{1 + 1}$ .

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Use the power rule $a^{m} a^{n} = a^{m + n}$ to combine exponents.

$f (x + 1) = 3 (x^{1 + 1} + x \cdot 1 + 1 x + 1 \cdot 1)$

Add $1$ and $1$ .

$f (x + 1) = 3 (x^{2} + x \cdot 1 + 1 x + 1 \cdot 1)$

Multiply $x$ by $1$ .

$f (x + 1) = 3 (x^{2} + x + 1 x + 1 \cdot 1)$

Multiply $x$ by $1$ .

$f (x + 1) = 3 (x^{2} + x + x + 1 \cdot 1)$

Multiply $1$ by $1$ .

$f (x + 1) = 3 (x^{2} + x + x + 1)$

Add $x$ and $x$ .

$f (x + 1) = 3 (x^{2} + 2 x + 1)$

Apply the distributive property.

$f (x + 1) = 3 x^{2} + 3 (2 x) + 3 \cdot 1$

Simplify.

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Multiply $2$ by $3$ .

$f (x + 1) = 3 x^{2} + 6 x + 3 \cdot 1$

Multiply $3$ by $1$ .

$f (x + 1) = 3 x^{2} + 6 x + 3$

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