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

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

Set up the composite result function.

$f (g (x))$

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

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

Simplify each term.

Apply the distributive property.

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

Multiply $3$ by $- 2$ .

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

Multiply $- 2$ by $2$ .

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

Subtract $4$ from $3$ .

$f (3 x^{2} + 2) = - 6 x^{2} - 1$