Find the Range of \( f(x)=\cos[x] \)
The range of
\[ f(x)=\cos[x] \]
for
\[
-\frac{\pi}{2}
is
(a) \(\{-1,1,0\}\)
(b) \(\{\cos1,\cos2,1\}\)
(c) \(\{\cos1,-\cos1,1\}\)
(d) \([-1,1]\)
Since
\[
-\frac{\pi}{2}
i.e.
\[
-1.57
Therefore, possible values of \([x]\) are
\[
-2,-1,0,1
\]
Hence,
\[
f(x)=\cos(-2),\cos(-1),\cos0,\cos1
\]
Since,
\[
\cos(-\theta)=\cos\theta
\]
therefore,
\[
\text{Range}=\{\cos2,\cos1,1\}
\]
\[
\boxed{\text{Correct Answer: (b)}}
\]