Calculus Examples

$f (z) = z^{8}$ , $g (x) = 3 x^{2} + 4$

Step 1

Set up the composite result function.

$g (f (z))$

Step 2

Evaluate $g (z^{8})$ by substituting in the value of $f$ into $g$ .

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

Step 3

Multiply the exponents in ${(z^{8})}^{2}$ .

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Step 3.1

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

$g (z^{8}) = 3 z^{8 \cdot 2} + 4$

Step 3.2

Multiply $8$ by $2$ .

$g (z^{8}) = 3 z^{16} + 4$