Question

is the function g(x)=x^3-x even odd or neither and why

Answer 1

g(x) = g(-x) for even

g(x) + g(-x) = 0 for odd

try g(1) and g(-1) and see what you get

Answer 2

I got 0 for both

Answer 3

well then, do you think that makes it even or odd?

a function is even if f(x) is the same as f(-x)

and a function is odd if f(x) is opposite of f(-x)

what is the case here?

Answer 4

well g(x) + g(-x) =0 so it is odd

Answer 5

true, however g(x) also equals g(-x), so it could be even

try g(2) and g(-2)

you'll get a non-zero answer and should clear things up

Answer 6

that would be 6 and -6 so it would be even because g(x) equals g(-x)

Answer 7

yep!