What is the domain of f(x)=x/(x^2-5x)?

1 Answer
Lovecraft
Sep 19, 2015

D = -oo < x < oo | x != 0, x!= 5 and x in RR

Explanation:

The domain is every value that x can take without having a math error (division by zero, logarithm of a null or negative number, even root of a negative number, etc.)

So the only caveat we have here is that the denominator mustn't be 0. Or
x^2 - 5x != 0

We can solve this using the quadratic formula, sum and product, or, just do the easy thing and factor it out.
x^2 - 5x != 0
x(x - 5) != 0

Since the product can't be zero, neither can, that is
x != 0
x - 5 != 0 rarr x != 5

So the domain D, is D = -oo < x < oo, x != 0, x!= 5 | x in RR
Or
D = -oo < x < 0 or 0 < x < 5 or 5 < x | x in RR
Or that same thing in set notation.

Related questions
See all questions in Domain and Range of a Function
Impact of this question
3185 views around the world
You can reuse this answer
Creative Commons License