Find f(g(x)) f(x)=3x^2 , g(x)=2x^3

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

Set up the composite result function.

$f (g (x))$

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

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

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

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

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

$f (2 x^{3}) = 3 (4 {(x^{3})}^{2})$

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

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

$f (2 x^{3}) = 3 (4 x^{3 \cdot 2})$

Multiply $3$ by $2$ .

$f (2 x^{3}) = 3 (4 x^{6})$

Multiply $4$ by $3$ .

$f (2 x^{3}) = 12 x^{6}$