MCQ
The range of $\text{f(x)}=\cos[\text{x}],$ for $-\frac{\pi}{2}<\text{x}<\frac{\pi}{2}$ is:
- A$\{-1,1,0\}$
- B$\{\cos1,\cos2,1\}$
- C{$\cos1,-\cos1,1$}
- D$[-1,1]$
Solution:
Since, $\text{f(x)}=\cos[\text{x}],$ where $\frac{-\pi}{2}<\text{x}<\frac{\pi}{2}$
$-\frac{\pi}{2}<\text{x}<\frac{\pi}{2}$
$\Rightarrow-1.57<\text{x}<1.57$
$\Rightarrow[\text{x}]\ \in\ \{-1,0,1,2\}$
Thus, $\cos[\text{x}]=\{\cos(-1),\cos0,\cos1,\cos2\}$
Range of $\text{f(x)}=\{\cos1,1,\cos2\}$
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