Precalculus Examples

Find $(f \cdot g) (x)$ when $f (x) = 2 x^{2}$ and $g (x) = 6 x$

Step 1

Evaluate $f \cdot g$ .

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Step 1.1

Replace the function designators in $f \cdot g$ with the actual functions.

$(2 x^{2}) \cdot (6 x)$

Step 1.2

Rewrite using the commutative property of multiplication.

$2 \cdot 6 x^{2} x$

Step 1.3

Multiply $x^{2}$ by $x$ by adding the exponents.

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Step 1.3.1

Move $x$ .

$2 \cdot 6 (x \cdot x^{2})$

Step 1.3.2

Multiply $x$ by $x^{2}$ .

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Step 1.3.2.1

Raise $x$ to the power of $1$ .

$2 \cdot 6 (x^{1} x^{2})$

Step 1.3.2.2

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

$2 \cdot 6 x^{1 + 2}$

Step 1.3.3

Add $1$ and $2$ .

$2 \cdot 6 x^{3}$

Step 1.4

Multiply $2$ by $6$ .

$12 x^{3}$

Step 2

Evaluate $f \cdot g$ at $x$ .

$12 {(x)}^{3}$

Step 3

Simplify $12 {(x)}^{3}$ .

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Step 3.1

Remove parentheses.

$12 {(x)}^{3}$

Step 3.2

Remove parentheses.

$12 x^{3}$