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

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

Step 1

Set up the composite result function.

$g (f (x))$

Step 2

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

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

Step 3

Simplify each term.

Apply the distributive property.

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

Multiply $2$ by $3$ .

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

Multiply $3$ by $3$ .

$g (2 x^{2} + 3) = 6 x^{2} + 9 - 2$

Step 4

Subtract $2$ from $9$ .

$g (2 x^{2} + 3) = 6 x^{2} + 7$