How are even and odd functions defined in n-dimensions? In my homework, we had to integrate f(x,y,z)= (x^2)z + (y^2)z + z^3 over a sphere centered at the origin. My answer came out to be 0 and I made the guess that it might be because f(x,y,z) was an odd function. Now, I don't know if this is true. Does this assumption hold: f(x) is odd if f(-x) = -f(x) f(x,y,z) is odd if f(-x,-y,-z) = -f(x,y,z) ? I'm thinking this might just mean it's odd across a plane.I just handed in my assignment and will have to wait 2 weeks before I know if what I did was right or wrong, so I'm asking here to speed things up!