1. The problem is to find the domain of the function $$f(x) = \frac{x - 1}{x^2 + 1}$$. 2. The domain of a function is the set of all real numbers for which the function is defined. 3. Since the function is a fraction, it is undefined where the denominator is zero. 4. Set the denominator equal to zero and solve: $$x^2 + 1 = 0$$ 5. Rearranging gives: $$x^2 = -1$$ 6. There is no real number $x$ such that $x^2 = -1$ because the square of a real number is always non-negative. 7. Therefore, the denominator is never zero for any real $x$. 8. Hence, the function is defined for all real numbers. 9. The domain of $$f(x)$$ is: $$\boxed{(-\infty, +\infty)}$$