Subject: Domain and Range
FROM: Stacey Hutchison
LEVEL: Secondary school (10-12)

What is the domain of:

f(x) = -1/(x + 4)

I have looked at this question and I think that the domain would be that x cannot = 4, XER. Am I even close to the right answer?

Hi Stacey,

To find the domain of a function you need to ask yourself the question "what x-values am I allowed to use". It's often easier to look at a function and ask yourself "what x-values am I NOT allowed to use". In this case, since division is involved, you know you cannot divide by zero. What x-value would lead to a division of zero? In this case x=-4. Hence the domain is any real number, EXCEPT x=-4.

Similarily, the domain of f(x) = -x / (x+1)(x-2) would be any x-value except x=-1 and x=2.

If you have a function with an even root in it, remember that you cannot take an even root of a negative number. As a result, in a function such as f(x) = sqrt(x-1) only x-values greater than x=1 are allowed, hence the domain is all x>1.

Hope this helps,

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