Let f :
Question:

Let $f:\left(-\frac{\pi}{2}, \frac{\pi}{2}\right) \rightarrow R$ be a function defined by $f(x)=\cos [x]$. Write range (f).

Solution:

Domain $=\left(\frac{-\pi}{2}, \frac{\pi}{2}\right)=(-1.57,1.57) \quad\left(\right.$ as $\left.\pi=\frac{22}{7}\right)$

So, $\cos [x]=\cos (-2)=\cos 2 \quad \forall x \in(-1.57,0)$

Also, $\cos 0=1$ for $x=0$

And $\cos [x]=\cos 1 \forall x \in(0,1.57)$

$\therefore$ Range $=\{1, \cos 1, \cos 2\}$

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