Algebraically determine whether the function j (x) = x^4-3x^2-4 is odd even or neither

We have the following definitions:

A function is even if, for each x in the domain of f, f ( - x) = f (x)

A function is odd if, for each x in the domain of f, f ( - x) = - f (x)

Let's see the given function:

j (x) = x ^ 4-3x ^ 2-4

j (-x) = ( - x) ^ 4-3 (-x) ^ 2-4

Rewriting:

j (-x) = (x) ^ 4-3 (x) ^ 2-4

j (-x) = j (x)

Answer:

The function is even