Function Notation Question 4

If $f(x)=3x+8 $ and $ g(x)=x^2-3x+4 $, which of the following expressions is equivalent to $f(x)-g(x) $ ?

$ -x^2+6x+4 $

$ -x^2+12 $

$ x^2+4 $

$ x^2-6x-4 $

Approach

Subtract the given functions. Make sure to distribute the negative sign, since we are subtracting all of $g(x)$.

$$f(x)=3x+8 \text{ and } g(x)=x^2-3x+4$$ $$ f(x)-g(x) $$ $$ =3x+8-(x^2-3x+4) $$ $$=3x+8-x^2+3x-4 $$ $$ = \boxed{-x^2+6x+4} $$