Question:
Write the range of the function $1(x)=\sin [x]$, where $\frac{-\pi}{4} \leq x \leq \frac{\pi}{4}$.
Solution:
Given: $f(x)=\sin [x]$, where $\frac{-\pi}{4} \leq x \leq \frac{\pi}{4}$.
$-\frac{\pi}{4} \leq x \leq \frac{\pi}{4}$
$\Rightarrow-7.85 \leq x \leq 0.785$
$\therefore x \in[-7.85,7.85]$
Or $x=\{0,1\}$
Thus, range of $f(x)=\sin [x]$ is
$\{\sin 0, \sin 1\}=\{0, \sin 1\}$