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# Functions Help

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The function f : $$\mathbb{R} \to \mathbb{R}$$ satisfies $$x^2 f(x) + f(1 - x) = -x^4 + 2x$$ for all real numbers x. Then f(x) can be uniquely determined for all values of x, except $$f(\alpha)$$ and $$f(\beta)$$ for some real numbers $$\alpha$$ and $$\beta$$. Compute $$\alpha^2 + \beta^2.$$

Thanks so much!

Apr 4, 2021

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$\alpha^2 + \beta^2 = \boxed{5}$

Apr 4, 2021
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