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: $f(x)=\dfrac{-1}{x^2+x^4}$

calculate f(-x):

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

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

If we have: $f(x)=\dfrac{-1}{x^2}+x^4$

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

f(-x) = f(x)

f(x) is even