Question

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

Answer 1

$$\begin{gathered} \text{Domain =}\left(\frac{-\mathrm{\pi }}{2},\frac{\mathrm{\pi }}{2}\right)\text{=}\left(-1.57,1.57\right)\text{(as π=}\frac{22}{7}\text{)} \\ \mathrm{So},\cos \left[x\right]=\cos \left(-2\right)=\cos 2\forall x\in \left(-1.57,0\right) \\ \mathrm{Also},\cos 0=1\mathrm{for}x=0 \\ \mathrm{And}\cos \left[x\right]=\cos 1\forall x\in \left(0,1.57\right) \\ \therefore \text{Range=}\left\{1,\cos 1,\cos 2\right\} \end{gathered}$$