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)#

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