Question

What is the domain and zeroes of `f(x) = (x^2 - x - 2)/(x^2-x)`?

Answer 1

The domain is all real numbers except 0 and 1. The zeroes are at x=2 and x=-1.

Explanation:

`x^2-x-2` = `(x-2)(x+1)`, so the zeroes are 2 and -1. The denominator `x^2-x` = x(x-1) has zeroes at 0 and 1. Since one can not divide by 0, the function is undefined at 0 and 1. It is defined everywhere else, so the domain excludes only 0 and 1.