# What is the domain and range of y = -(sqrt(-x))?

Aug 7, 2017

The domain and range both in interval notation are $\left(- \infty , 0\right]$ i.e. domain is given by $x \le 0$ and range is givren by $y \le 0$.
As $y = - \sqrt{- x}$, it is apparent that you cannot have square root of a negative number.
Hence $- x \ge 0$ or in other words $x \le 0$ - which is the domain of $x$ and in interval notation it is $\left(- \infty , 0\right]$.
Now given $x \le 0$, the range of values that $y$ can have is $\left(- \infty , 0\right]$ and hence range is $y \le 0$