Solve the Function Operation f(x)=3x^2-4 , g(x)=x+2 , (f-g)(x)

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

Evaluate $f - g$ .

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

$(3 x^{2} - 4) - (x + 2)$

Simplify each term.

Apply the distributive property.

$3 x^{2} - 4 - x - 1 \cdot 2$

Multiply $- 1$ by $2$ .

$3 x^{2} - 4 - x - 2$

Subtract $2$ from $- 4$ .

$3 x^{2} - x - 6$

Evaluate $f - g$ at $x$ .

$3 {(x)}^{2} - (x) - 6$

Simplify $3 {(x)}^{2} - (x) - 6$ .

Remove parentheses.

$3 {(x)}^{2} - (x) - 6$

Multiply $- 1$ by $x$ .

$3 x^{2} - x - 6$