Question

Please help! Determine algebraically whether h(x)=x^3-x^2-x is odd, even, or neither.

Answer 1

Neither. Note the mix of even and odd exponents.

Answer 2

An even function is where h(-a) = h(a).
An odd function is where h(-a) = -h(a). Try substituting x= -x into the equation and seeing if they are equal.

Answer 3

Thanks guys! :)

Answer 4

The sum of an even function and an odd function is neither even nor odd. This function can be broken into \[h(x)=x^3-x^2-x =(x^3-x)-x^2\]

Answer 5

x^3-x is odd, x^2 is even.