Home > Algebra > Domain and Range of a Function

How do you find the domain of #sqrt(x - 1)/(x + 4)#?

Answer 1

Hazel Anglin

#[0, oo)#

Square roots have to be either zero or positive, so

#x-1>=0 -> x>=1# is part of our domain.

But division by zero might not exist for us either:

#x+4 ne 0#

#x ne -4#

From the first portion of the problem, where we ensure that we only have a positive root, #x=-4# is already excluded from the domain, so, this part of the problem only reinforces that #x>=0#.

The domain is then #[0, oo)#

By signing up, you agree to our Terms of Service and Privacy Policy

Answer 2

Julia Adams

Set the expression inside the square root greater than or equal to zero, and the denominator not equal to zero. The resulting conditions determine the domain.

By signing up, you agree to our Terms of Service and Privacy Policy

Answer from HIX Tutor

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.