Question

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

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

Answer 1

Answer: (C)

$\because [x]$ is an integer, $\cos (-x)=\cos x$ and
$\cos \left(\frac{\pi }{2}\right)=0,\cos 2\left(\frac{\pi }{2}\right)=-1,\cos 0\left(\frac{\pi }{2}\right)=1,\cos 3\left(\frac{\pi }{2}\right)=0$
Hence range $=\{-1,0,1\}$