Find g(f(x)) f(x)=4x^2+3x+5 , g(x)=3x-7

$f (x) = 4 x^{2} + 3 x + 5$ , $g (x) = 3 x - 7$

Step 1

Set up the composite result function.

$g (f (x))$

Step 2

Evaluate $g (4 x^{2} + 3 x + 5)$ by substituting in the value of $f$ into $g$ .

$g (4 x^{2} + 3 x + 5) = 3 (4 x^{2} + 3 x + 5) - 7$

Step 3

Simplify each term.

Apply the distributive property.

$g (4 x^{2} + 3 x + 5) = 3 (4 x^{2}) + 3 (3 x) + 3 \cdot 5 - 7$

Simplify.

Multiply $4$ by $3$ .

$g (4 x^{2} + 3 x + 5) = 12 x^{2} + 3 (3 x) + 3 \cdot 5 - 7$

Multiply $3$ by $3$ .

$g (4 x^{2} + 3 x + 5) = 12 x^{2} + 9 x + 3 \cdot 5 - 7$

Multiply $3$ by $5$ .

$g (4 x^{2} + 3 x + 5) = 12 x^{2} + 9 x + 15 - 7$

Step 4

Subtract $7$ from $15$ .

$g (4 x^{2} + 3 x + 5) = 12 x^{2} + 9 x + 8$