What is the domain of f(x)= x/(x^2+1)?

1 Answer
VNVDVI
May 14, 2018

All real numbers; (-oo, oo)

Explanation:

When dealing with these rational functions in the form f(x)=p(x)/q(x), p(x), q(x) are both polynomials, the first thing we should check for is values of x for which the denominator equals 0.

The domain doesn't include these values due to division by 0. So, for f(x)=x/(x^2+1), let's see whether such values exist:

Set the denominator equal to 0 and solve for x:

x^2+1=0

x^2=-1

There are no real solutions; thus, the domain is all real numbers, that is, (-oo, oo)

Related questions
See all questions in Domain and Range of a Function
Impact of this question
13263 views around the world
You can reuse this answer
Creative Commons License