Question

How do you determine if `f(x)= x^2+x` is an even or odd function?

Answer 1

I would say neither odd or even.

Explanation:

If it is odd then: `f(-x)=-f(x)` for example the sine function;
if it is even then `f(-x)=f(x)` as for the cossine function.
In our case let us choose `x=2`
`f(x)=f(2)=(2)^2+(2)=4+2=6`
So, let us check:
`f(-x)=f(-2)=(-2)^2+(-2)=4-2=2`
`-f(x)=-f(2)=-[(2)^2+2]=-6`

`f(-x)!=f(x)!=-f(x)`
So no condition is satisfied!