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

1 Answer
Prof_S
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.

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