Find g(f(x)) g(x)=x^2+7x-3 , f(x)=x^3

$g (x) = x^{2} + 7 x - 3$ , $f (x) = x^{3}$

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 $g$ .

$g (x^{3}) = {(x^{3})}^{2} + 7 (x^{3}) - 3$

Step 3

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

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

$g (x^{3}) = x^{3 \cdot 2} + 7 (x^{3}) - 3$

Multiply $3$ by $2$ .

$g (x^{3}) = x^{6} + 7 (x^{3}) - 3$

$g (x^{3}) = x^{6} + 7 x^{3} - 3$