Find f(g(x)) f(x)=3x+2 , g(x)=4x^2+3

$f (x) = 3 x + 2$ , $g (x) = 4 x^{2} + 3$

Step 1

Set up the composite result function.

$f (g (x))$

Step 2

Evaluate $f (4 x^{2} + 3)$ by substituting in the value of $g$ into $f$ .

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

Step 3

Simplify each term.

Apply the distributive property.

$f (4 x^{2} + 3) = 3 (4 x^{2}) + 3 \cdot 3 + 2$

Multiply $4$ by $3$ .

$f (4 x^{2} + 3) = 12 x^{2} + 3 \cdot 3 + 2$

Multiply $3$ by $3$ .

$f (4 x^{2} + 3) = 12 x^{2} + 9 + 2$

Step 4

Add $9$ and $2$ .

$f (4 x^{2} + 3) = 12 x^{2} + 11$