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Determine if the function is even, odd, or neither.g(x) = x12+ x5

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An even function is defined as function that fullfils:


f(-x)=f(x)

An odd function is defined as a function that fullfils:


f(-x)=-f(x)

Then we need to find if the function fullfuls either of the definitions above:


\begin{gathered} g(-x)=(-x)^(12)+(-x)^5 \\ =x^(12)-x^5 \end{gathered}

Therefore, the function does not fullfils neither of the definitions, hence the function is not an even or odd one.

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