Is the following function even, odd or neither?

Question

Is the following function even, odd or neither ?

$$[2x]$$

Shall I divide the argument into when it belongs to $\mathbb{Z}$ and when it belongs to $\mathbb{R}$ \ $\mathbb{Z}$?And what about if the argument inside the step function is a trigonometric function ?

thanks!

Answer 1

• It's not even because $f(\frac{1}{2})=1$, where as $f(-\frac{1}{2})=-1$.

• It's not odd, because $f(0.1)=0$ where as $-f(-0.1)=-(-1)=1$.