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Mathematics
Mathematics
Problem
Consider
f
(
x
)
=
sin
−
1
[
2
x
]
+
cos
−
1
(
[
x
]
−
1
)
f(x) = \sin^{-1}[2x] + \cos^{-1}([x] - 1)
f
(
x
)
=
sin
−
1
[
2
x
]
+
cos
−
1
([
x
]
−
1
)
(where
[
.
]
[.]
[
.
]
denotes greatest integer function.) If domain of
f
(
x
)
f(x)
f
(
x
)
is
[
a
,
b
]
[a, b]
[
a
,
b
]
and the range of
f
(
x
)
f(x)
f
(
x
)
is
c
,
d
{c, d}
c
,
d
, then
a
+
b
+
2
d
c
a + b + \frac{2d}{c}
a
+
b
+
c
2
d
is equal to (where
c
<
d
c < d
c
<
d
)
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