Question

Is the function `f(x)=x^4-6^-4+3x^2` even, odd or neither?

Answer 1

The function `f` is even.

Explanation:

An even function `f` is defined such that `f(-x)=f(x)` for all `x` in the domain of `f`. Using this definition, we examine `f(-x)`:
`f(-x)=(-x)^4-6^-4+3(-x)^2`
`f(-x)=x^4-6^-4+3x^2`
`f(-x)=f(x)`
Since `f(-x)=f(x)`, we have shown that the function `f` is indeed even.