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Problem
Problem
Let
f
:
[
π
3
,
2
π
3
]
→
[
0
,
4
]
f: \left[\frac{\pi}{3}, \frac{2\pi}{3}\right] \rightarrow [0, 4]
f
:
[
3
π
,
3
2
π
]
→
[
0
,
4
]
be a function defined as
f
(
x
)
=
3
sin
x
−
cos
x
+
2
f(x) = \sqrt{3} \sin x - \cos x + 2
f
(
x
)
=
3
sin
x
−
cos
x
+
2
. Then
f
−
1
(
x
)
f^{-1}(x)
f
−
1
(
x
)
is given by (a)
sin
−
1
(
x
−
2
2
)
−
π
6
\sin^{-1}\left(\frac{x-2}{2}\right) - \frac{\pi}{6}
sin
−
1
(
2
x
−
2
)
−
6
π
(b)
sin
−
1
(
x
−
2
2
)
+
π
6
\sin^{-1}\left(\frac{x-2}{2}\right) + \frac{\pi}{6}
sin
−
1
(
2
x
−
2
)
+
6
π
(c)
2
π
3
+
cos
−
1
(
x
−
2
2
)
\frac{2\pi}{3} + \cos^{-1}\left(\frac{x-2}{2}\right)
3
2
π
+
cos
−
1
(
2
x
−
2
)
(d) None of these
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