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Mathematics
Mathematics
Problem
If
f
(
x
)
=
sin
−
1
x
f(x) = \sin^{-1} x
f
(
x
)
=
sin
−
1
x
and
g
(
x
)
=
[
sin
(
cos
x
)
]
+
[
cos
(
sin
x
)
]
g(x) = [\sin(\cos x)] + [\cos(\sin x)]
g
(
x
)
=
[
sin
(
cos
x
)]
+
[
cos
(
sin
x
)]
, then range of
f
(
g
(
x
)
)
f(g(x))
f
(
g
(
x
))
is (where
[
⋅
]
[\,\cdot\,]
[
⋅
]
denotes greatest integer function) a.
{
−
π
2
,
π
2
}
\left\{\frac{-\pi}{2}, \frac{\pi}{2}\right\}
{
2
−
π
,
2
π
}
b.
{
−
π
2
,
0
}
\left\{\frac{-\pi}{2}, 0\right\}
{
2
−
π
,
0
}
c.
{
0
,
π
2
}
\left\{0, \frac{\pi}{2}\right\}
{
0
,
2
π
}
d.
{
−
π
2
,
0
,
π
2
}
\left\{-\frac{\pi}{2}, 0, \frac{\pi}{2}\right\}
{
−
2
π
,
0
,
2
π
}
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