Find f(g(x)) f(x)=2x^2-5x g(x)=3x^3

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

Set up the composite result function.

$f (g (x))$

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

$f (3 x^{3}) = 2 {(3 x^{3})}^{2} - 5 (3 x^{3})$

Simplify each term.

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

$f (3 x^{3}) = 2 (3^{2} {(x^{3})}^{2}) - 5 (3 x^{3})$

Raise $3$ to the power of $2$ .

$f (3 x^{3}) = 2 (9 {(x^{3})}^{2}) - 5 (3 x^{3})$

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

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

$f (3 x^{3}) = 2 (9 x^{3 \cdot 2}) - 5 (3 x^{3})$

Multiply $3$ by $2$ .

$f (3 x^{3}) = 2 (9 x^{6}) - 5 (3 x^{3})$

Multiply $9$ by $2$ .

$f (3 x^{3}) = 18 x^{6} - 5 (3 x^{3})$

Multiply $3$ by $- 5$ .

$f (3 x^{3}) = 18 x^{6} - 15 x^{3}$