Question

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

Answer 1

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.