Question

The range of $f\left(x\right)=\cos \frac{\pi \left[x\right]}{2}$ is

• A. $\{0,1\}$
• B. $\{-1,1\}$
• C. $\{-1,0,1\}$
• D. $[-1,1]$

Answer 1

The correct option is C $\{-1,0,1\}$

range of $\left[x\right]$ is all integers

so $\frac{\pi }{2}\left[x\right]$ is multiples of $\frac{\pi }{2}$

so range of f(x) is $-1,0,1$