How to determine if a function is even, odd, neither

Question

Determine if the functions are even, odd or neither.

g(x) = (x-x²) / (x-1)

Answer 1

For x ≠ 1, g(x) = (x - x²)/(x - 1) = x(1 - x)/(x - 1) = -x

If g(x) = -x, it would be an odd function, as g(-x) = - (-x) = x

However, because g(x) does not exist at x = 1 but does exist at -1, this is not an odd function.

Answer 2

Even function, f(x) = f(-x)

Odd function, -f(x) = f(-x)