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

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

Set up the composite result function.

$f (g (x))$

Evaluate $f (3 x^{2} - 5 x - 2)$ by substituting in the value of $g$ into $f$ .

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

Combine the opposite terms in $(3 x^{2} - 5 x - 2) + 2$ .

Add $- 2$ and $2$ .

$f (3 x^{2} - 5 x - 2) = 3 x^{2} - 5 x + 0$

Add $3 x^{2} - 5 x$ and $0$ .

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