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

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

Step 1

Evaluate $h - g$ .

Replace the function designators in $h - g$ with the actual functions.

$(3 x^{2} + 1) - (- 2 x + 3)$

Simplify each term.

Apply the distributive property.

$3 x^{2} + 1 - (- 2 x) - 1 \cdot 3$

Multiply $- 2$ by $- 1$ .

$3 x^{2} + 1 + 2 x - 1 \cdot 3$

Multiply $- 1$ by $3$ .

$3 x^{2} + 1 + 2 x - 3$

Subtract $3$ from $1$ .

$3 x^{2} + 2 x - 2$

Step 2

Evaluate $h - g$ at $x$ .

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

Step 3

Simplify $3 {(x)}^{2} + 2 (x) - 2$ .

Remove parentheses.

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

Multiply $2$ by $x$ .

$3 x^{2} + 2 x - 2$