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

Oct 17, 2015

The domain is the open interval $\left\{x \in \mathbb{R} : 0 < x < 1\right\} = \left(0 , 1\right)$

#### Explanation:

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