Algebra Examples

$f (x) = 2 x^{4}$ , $g (x) = 3 x^{8}$ , $h (x) = x^{6}$

Step 1

Set up the composite result function.

$g (f (x))$

Step 2

Evaluate $g (2 x^{4})$ by substituting in the value of $f$ into $g$ .

$g (2 x^{4}) = 3 {(2 x^{4})}^{8}$

Step 3

Apply the product rule to $2 x^{4}$ .

$g (2 x^{4}) = 3 (2^{8} {(x^{4})}^{8})$

Step 4

Raise $2$ to the power of $8$ .

$g (2 x^{4}) = 3 (256 {(x^{4})}^{8})$

Step 5

Multiply the exponents in ${(x^{4})}^{8}$ .

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Step 5.1

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

$g (2 x^{4}) = 3 (256 x^{4 \cdot 8})$

Step 5.2

Multiply $4$ by $8$ .

$g (2 x^{4}) = 3 (256 x^{32})$

Step 6

Multiply $256$ by $3$ .

$g (2 x^{4}) = 768 x^{32}$