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Use the definition of Odd and Even functions to determine whether each of the following functions is Odd, Even, or neither. Must show your work for credit II!1) \( f(x)=\frac{x}{1-x^{3}} \)2) \( f(x)=\frac{x^{2}}{1+x} \)3) \( \quad f(x)=x-|x| \) |
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Answer» (1) f(x) = \(\frac{x}{1-x^3}\) f(-x) = \(\frac{-x}{1-(-x)^3}\) = \(\frac{-x}{1+x^3}\) ≠ -f(x) or f(x) ∴ f(x) is neither even nor odd function. (2) f(x) = \(\frac{x^2}{1+x}\) ∴ f(-x) = \(\frac{(-x^2)}{1+(-x)}\) = \(\frac{x^2}{1-x}\) ≠ -f(x) or f(x). (3) f(x) = x-|x| ∴ f(-x) = -x-|-x| = -x-|x| = -(x+|x|) ≠ -f(x) or f(x) ∴ f(x) is neither even nor odd function. |
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