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}