Solve the Function Operation f(x)=7x+11 g(x)=-2x+3 h(x)=3x^2+1 (gof)(x)

$f (x) = 7 x + 11$ $g (x) = - 2 x + 3$ $h (x) = 3 x^{2} + 1$ $(g o f) (x)$

Step 1

Set up the composite result function.

$g (f (x))$

Step 2

Evaluate $g (7 x + 11)$ by substituting in the value of $f$ into $g$ .

$g (7 x + 11) = - 2 (7 x + 11) + 3$

Step 3

Simplify each term.

Apply the distributive property.

$g (7 x + 11) = - 2 (7 x) - 2 \cdot 11 + 3$

Multiply $7$ by $- 2$ .

$g (7 x + 11) = - 14 x - 2 \cdot 11 + 3$

Multiply $- 2$ by $11$ .

$g (7 x + 11) = - 14 x - 22 + 3$

Step 4

Add $- 22$ and $3$ .

$g (7 x + 11) = - 14 x - 19$