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

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

Set up the composite result function.

$f (g (x))$

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

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

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

Add $- 3$ and $3$ .

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

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

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