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

 Oct 7, 2023
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The function f(x) is undefined when any of the denominators are equal to 0. Therefore, we need to solve the following equations:

x^2 + 7 = 0 x^3 - x^4 = 0 x^2 - 3x + 2 = 0

The first equation has no real solutions. The second equation can be factored as x(x2−x)=0, which has solutions x=0 and x=1. The third equation can be factored as (x−2)(x−1)=0, which has solutions x=1 and x=2.

Therefore, the domain of f(x) is all real numbers except for x=0, x=1, and x=2. The sum of these three numbers is 0+1+2=3​.

 Oct 7, 2023

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