Math help, how to tell even,odd or neither functions?

Question

How do you numerically determine whether

f(x) = (x^4) / (x^2 - 1)

is an even, odd, or neither even nor odd function?

and how do you determine it symbolically?

Please explain how you did it as well as showing the work. Thank you!

Answer 1

Odd function:

f(-x) = - f(x)

f(-x) = (-x)^4 / ((-x)^2 - 1) = x^4 / (x^2 -1)

-f(x) = -x^4 / (x^2-1)

So, f(-x) ≠ -f(x)

f(x) is not an odd function

Even function:

f(x) = f(-x)

f(x) =(x^4) / (x^2 - 1)

f(-x) = (-x)^4 / ((-x)^2 - 1) = x^4 / (x^2 -1)

f(x)=f(-x)

So, this is an even function.

If neither of the above conditions are met, it is neither an odd nor an even function.

Answer 2

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