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

1 Answer
Jan 12, 2016

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.