Precalculus Examples

If $f (x) = 6 x^{2}$ and $g (x) = 8 x^{2}$ ; what is $(f \cdot g) (x)$ ?

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.

$(6 x^{2}) \cdot (8 x^{2})$

Step 1.2

Rewrite using the commutative property of multiplication.

$6 \cdot 8 x^{2} x^{2}$

Step 1.3

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

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Step 1.3.1

Move $x^{2}$ .

$6 \cdot 8 (x^{2} x^{2})$

Step 1.3.2

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

$6 \cdot 8 x^{2 + 2}$

Step 1.3.3

Add $2$ and $2$ .

$6 \cdot 8 x^{4}$

Step 1.4

Multiply $6$ by $8$ .

$48 x^{4}$

Step 2

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

$48 {(x)}^{4}$

Step 3

Simplify $48 {(x)}^{4}$ .

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Step 3.1

Remove parentheses.

$48 {(x)}^{4}$

Step 3.2

Remove parentheses.

$48 x^{4}$