Find g(f(x)) f(x)=2x^2-7x+6 g(x)=4x+10

$f (x) = 2 x^{2} - 7 x + 6$ $g (x) = 4 x + 10$

Step 1

Set up the composite result function.

$g (f (x))$

Step 2

Evaluate $g (2 x^{2} - 7 x + 6)$ by substituting in the value of $f$ into $g$ .

$g (2 x^{2} - 7 x + 6) = 4 (2 x^{2} - 7 x + 6) + 10$

Step 3

Simplify each term.

Apply the distributive property.

$g (2 x^{2} - 7 x + 6) = 4 (2 x^{2}) + 4 (- 7 x) + 4 \cdot 6 + 10$

Simplify.

Multiply $2$ by $4$ .

$g (2 x^{2} - 7 x + 6) = 8 x^{2} + 4 (- 7 x) + 4 \cdot 6 + 10$

Multiply $- 7$ by $4$ .

$g (2 x^{2} - 7 x + 6) = 8 x^{2} - 28 x + 4 \cdot 6 + 10$

Multiply $4$ by $6$ .

$g (2 x^{2} - 7 x + 6) = 8 x^{2} - 28 x + 24 + 10$

Step 4

Add $24$ and $10$ .

$g (2 x^{2} - 7 x + 6) = 8 x^{2} - 28 x + 34$