Precalculus Examples

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

Step 1

Set up the composite result function.

$f (g (x))$

Step 2

Evaluate $f (x + 1)$ by substituting in the value of $g$ into $f$ .

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

Step 3

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

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

Step 4

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

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Step 4.1

Apply the distributive property.

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

Step 4.2

Apply the distributive property.

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

Step 4.3

Apply the distributive property.

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

Step 5

Simplify and combine like terms.

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Step 5.1

Simplify each term.

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Step 5.1.1

Multiply $x$ by $x$ .

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

Step 5.1.2

Multiply $x$ by $1$ .

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

Step 5.1.3

Multiply $x$ by $1$ .

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

Step 5.1.4

Multiply $1$ by $1$ .

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

Step 5.2

Add $x$ and $x$ .

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

Step 6

Apply the distributive property.

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

Step 7

Simplify.

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Step 7.1

Multiply $2$ by $3$ .

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

Step 7.2

Multiply $3$ by $1$ .

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

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