Solve the Function Operation f(x)=6x^2+x , g(x)=x+1 , f(x)-g(x)

$f (x) = 6 x^{2} + x$ , $g (x) = x + 1$ , $f (x) - g (x)$

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

$(6 x^{2} + x) - (x + 1)$

Simplify $(6 x^{2} + x) - (x + 1)$ .

Simplify each term.

Apply the distributive property.

$6 x^{2} + x - x - 1 \cdot 1$

Multiply $- 1$ by $1$ .

$6 x^{2} + x - x - 1$

Combine the opposite terms in $6 x^{2} + x - x - 1$ .

Subtract $x$ from $x$ .

$6 x^{2} + 0 - 1$

Add $6 x^{2}$ and $0$ .

$6 x^{2} - 1$