Question

How do you find the domain of the following functions `f(x)= ln(x-x^2)`?

Answer 1

The domain is the open interval `{x in RR:0 < x < 1}=(0,1)`

Explanation:

Since the domain of `ln(x)` is `{x in RR:x>0}`, it follows that we require `x-x^2>0\leftrightarrow x(1-x)>0\leftrightarrow 0 < x < 1`. Hence the domain of `f(x)=ln(x-x^2)` is `{x in RR:0 < x < 1}=(0,1)`.