Question

Determine whether the function f(x) -1 / x^2 + x^4 is even odd or neither

Answer 1

If f(-x) = f(x) then the function is even.

If f(-x) = -f(x) then the function is odd.

We have:
`f(x)=(-1)/(x^2+x^4)`

calculate f(-x):

`f(-x)=(-1)/((-x)^2+(-x)^4)=(-1)/((-1x)^2+(-1x)^4)\\\\=(-1)/((-1)^2x^2+(-1)^4x^4)=(-1)/(1x^2+1x^4)=(-1)/(x^2+x^4)=f(x)`

f(-x) = f(x), therefore your answer: The function f(x) is even.

If we have:
`f(x)=(-1)/(x^2)+x^4`

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

f(-x) = f(x)

f(x) is even