# How do you find the domain of f (x) = sqrt( -x) / [(x - 3) (x + 5)]?

Apr 4, 2018

What is the domain? The domain is the range of numbers when substituted gives a valid answer and not undefined

Now, it would be undefined if the denominator was equal to 0

So, $\left(x - 3\right) \left(x + 5\right)$ must be equal to 0 which happens when $x = 3 , - 5$

So these numbers are not part of the domain

This would also be undefined if the number under the root was negative.

So for $- x$ to be negative, $x$ must be positive.

So all positive numbers are also not part of the domain

So as we can see, the numbers that make it undefined are all positive numbers

Hence the domain is all negative numbers inclusive of 0.