Write the range of the function f(x) = cos [x],
Question:

Write the range of the function $1(x)=\cos [x]$, where $\frac{-\pi}{2}<x<\frac{\pi}{2}$.

Solution:

Since $f(x)=\cos [x]$, where $\frac{-\pi}{2}<x<\frac{\pi}{2}$

$-\frac{\pi}{2}<x<\frac{\pi}{2}$

$\Rightarrow-1.57<x<1.57$

$\Rightarrow[x] \in\{-1,0,1,2\}$

Thus, $\cos [x]=\{\cos (-1), \cos 0, \cos 1, \cos 2\}$.

Range of $f(x)=\{\cos 1,1, \cos 2\}$.