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Mathematics
Mathematics
Problem
The range of the function
f
(
x
)
=
sin
−
1
[
x
2
+
1
2
]
+
cos
−
1
[
x
2
−
1
2
]
f(x) = \sin^{-1} \left[ x^2 + \frac{1}{2} \right] + \cos^{-1} \left[ x^2 - \frac{1}{2} \right]
f
(
x
)
=
sin
−
1
[
x
2
+
2
1
]
+
cos
−
1
[
x
2
−
2
1
]
, is (Note:
[
k
]
[k]
[
k
]
denotes greatest integer function less than or equal to
k
k
k
) (a)
{
π
2
,
π
}
\{\frac{\pi}{2}, \pi\}
{
2
π
,
π
}
(b)
{
π
}
\{\pi\}
{
π
}
(c)
{
π
2
}
\{\frac{\pi}{2}\}
{
2
π
}
(d)
{
π
4
,
π
2
}
\{\frac{\pi}{4}, \frac{\pi}{2}\}
{
4
π
,
2
π
}
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