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

May 14, 2018

All real numbers; $\left(- \infty , \infty\right)$

#### Explanation:

When dealing with these rational functions in the form $f \left(x\right) = p \frac{x}{q} \left(x\right) , p \left(x\right) , q \left(x\right)$ 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 $f \left(x\right) = \frac{x}{{x}^{2} + 1} ,$ 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, $\left(- \infty , \infty\right)$