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Mathematics
Mathematics
Problem
Let
f
(
x
)
=
sin
−
1
∣
sin
x
∣
+
cos
−
1
(
cos
x
)
f(x) = \sin^{-1} |\sin x| + \cos^{-1} (\cos x)
f
(
x
)
=
sin
−
1
∣
sin
x
∣
+
cos
−
1
(
cos
x
)
. Which of the following statement(s) is/are TRUE? a.
f
(
f
(
3
)
)
=
π
f(f(3)) = \pi
f
(
f
(
3
))
=
π
b.
f
(
x
)
f(x)
f
(
x
)
is periodic with fundamental period
2
π
2\pi
2
π
c.
f
(
x
)
f(x)
f
(
x
)
is neither even nor odd d. Range of
f
(
x
)
f(x)
f
(
x
)
is
[
0
,
2
π
]
[0, 2\pi]
[
0
,
2
π
]
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