Is the function $f(x)=-5x^4-3x^-4-2$ even, odd or neither?

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Answer 1 · 2015-10-02T19:33:06

The function is even.

$f(x) = -5x^4-3x^-4-2$

The domain of $f$ is $RR-{0}$

For any $x$ in the domain, $-x$ is also in the domain and:

$f(-x) = -5(-x)^4-3(-x)^-4-2$

$= -5x^4-3x^-4-2$

$= f(x)$

So $f$ is even.

We have used $(-x)^4 = x^4$ and

$(-x)^-4 = 1/(-x)^4 = 1/x^4=x^-4$ .

Is the function f(x)=-5x^4-3x^-4-2f(x)=-5x^4-3x^-4-2 even, odd or neither?