Question

PLEASE HELP ASAP!

Let f(x)=x²-x-12 and g(x)= x -4.
What value can the expression (f/g)(x) never equal?

Answer 1

7

Explanation:

This function can never equal 0. Why? well here:

(f/g)(x) also just means
`(f(x))/(g(x))`. In this case, we get
`(x^2-x-12)/(x-4)` Or
`((x+3)(x-4))/(x-4)`. It seems like you can cancel out x-4 and bam, you get x+3 and any value should work.

However, x can never equal 4 because 4 leads to a case where you divide by 0. This is called discontinuity. Thus, the value you can't get is x=4, or 7 because when you plug 4 in, you get 0/0. Otherwise, any other real value is defined by x+3.