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Let $$e(x)$$ be an even function, and let $$o(x)$$ be an odd function, such that $$e(x) + o(x) = \frac{6}{x + 2} + x^2 + 2^x$$ for all real numbers $$x.$$ Find $$o(1).$$

Apr 22, 2019

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$$\text{If you have a function }g(x) \text{ which is neither even nor odd (such as }2^x)\\ g_e(x)= \dfrac{g(x)+g(-x)}{2} \text{ is even and }\\ g_o(x) = \dfrac{g(x)-g(-x)}{2} \text{ is odd and }\\ g_e(x) + g_o(x) = g(x)$$

$$\text{Apply this to the two terms of the expression that are neither even nor odd}$$

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Apr 22, 2019