Question

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

Answer 1

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)`