Calculus Examples

$f (x) = x^{3}$ , $g (x) = x^{2} + 5 x - 6$

Step 1

Set up the composite result function.

$g (f (x))$

Step 2

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

$g (x^{3}) = {(x^{3})}^{2} + 5 (x^{3}) - 6$

Step 3

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

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Step 3.1

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

$g (x^{3}) = x^{3 \cdot 2} + 5 (x^{3}) - 6$

Step 3.2

Multiply $3$ by $2$ .

$g (x^{3}) = x^{6} + 5 (x^{3}) - 6$

$g (x^{3}) = x^{6} + 5 x^{3} - 6$