Is the function $f (x) = x^{4} + 3 x^{- 4} + 2 x^{- 1}$ $f(x)=x^4+3x^-4+2x^-1$ even, odd or neither?

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Answer 1 · 2015-10-29T20:13:20

This function is neither even nor odd.

To find if a function is even or odd or neither we have to calculete $f (- x)$ $f(-x)$ and see how it compares to $f (x)$ $f(x)$

In this case we have:
$f (- x) = {(- x)}^{4} + 3 {(- x)}^{- 4} + 2 {(- x)}^{- 1}$ $f(-x)=(-x)^4+3(-x)^-4+2(-x)^(-1)$

$f (- x) = x^{4} + 3 x^{- 4} - 2 x^{- 1}$ $f(-x)=x^4+3x^(-4)-2x^(-1)$

So we see that $f (- x) \neq f (x)$ $f(-x)!=f(x)$ and $f (- x) \neq - f (x)$ $f(-x)!=-f(x)$ , so $f (x)$ $f(x)$ is neither even nor odd.

Is the function f(x)=x^4+3x^-4+2x^-1f(x)=x4+3x−4+2x−1f(x)=x^4+3x^-4+2x^-1 even, odd or neither?