Question

The range of the function $f\left(x\right)=\cos \left[x\right]$ for $-\frac{\pi }{2}<x<\frac{\pi }{2}$ is ([•] denotes Greatest Integer Function)

• A. [–1, 1]
• B. {cos 1, – cos 1, 1}
• C. {cos 2, cos 1, 1}
• D. {– 1, 1, 0}

Answer 1

The correct option is C

{cos 2, cos 1, 1}

$-\frac{\pi }{2}<x<\frac{\pi }{2}\Rightarrow \left[x\right]=-2,-1,0,1$

$\Rightarrow f\left(x\right)=\cos \left[x\right]$

$=\cos (-2),\cos (-1),\cos \left(0\right),\cos 1$

$=\cos 2,\cos 1,1$