Find the sum of all real numbers $x$ that are not in the domain of the function $$f(x) = \frac{1}{x^2+7} + \frac{1}{x^3 - x^4} + \frac{1}{x^2 - 3x + 2}.$$

Answer 1

The function is defined unless a denominator is equal to zero. The first denominator, $x^2+7$, is never zero. The second denominator, $x^3 - x^4 = x^3(1 - x)$, is zero either when $x = 0$ or $x = 1$. The third denominator is zero when $x = 2$ or $x = 1$. Thus the function is defined for all $x$ except $x = 0, 1, 2$. The sum of these three real numbers is $0+1+2=\boxed{3}.$