Question

I have a question about the symmetry of graphs, but maybe it's more of a simple factoring question...

Why is f(x)=x+(1/x) odd, while h(x)=x-x^2 is neither even nor odd?

I understand that f(-x)=-x-1/x=-(x+1/x)=-f(x) is odd because f(x)=f(-x).

Then for h(-x)=-x-x^2...why can't you factor out the negative in this question like the previous one? But my textbook leaves it like this and says it's neither even nor odd...

Answer 1

h(x) = x - x^2
h(-x) = -x -x^2
but x is not -x so that part is odd
while -x^2 is -x^2 so that part is even

for odd I needed
h(-x) = -x + x^2 = -(x-x^2)
for even I needed
h(-x) = x - x^2