Algebra Examples

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

Step 1

Set up the composite result function.

$g (f (x))$

Step 2

Evaluate $g (3 x^{2})$ by substituting in the value of $f$ into $g$ .

$g (3 x^{2}) = 2 {(3 x^{2})}^{3}$

Step 3

Apply the product rule to $3 x^{2}$ .

$g (3 x^{2}) = 2 (3^{3} {(x^{2})}^{3})$

Step 4

Raise $3$ to the power of $3$ .

$g (3 x^{2}) = 2 (27 {(x^{2})}^{3})$

Step 5

Multiply the exponents in ${(x^{2})}^{3}$ .

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Step 5.1

Apply the power rule and multiply exponents, ${(a^{m})}^{n} = a^{m n}$ .

$g (3 x^{2}) = 2 (27 x^{2 \cdot 3})$

Step 5.2

Multiply $2$ by $3$ .

$g (3 x^{2}) = 2 (27 x^{6})$

Step 6

Multiply $27$ by $2$ .

$g (3 x^{2}) = 54 x^{6}$