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Mathematics
Mathematics
Problem
Let
f
(
x
)
=
x
2
−
2
a
x
+
a
−
2
f(x) = x^2 - 2ax + a - 2
f
(
x
)
=
x
2
−
2
a
x
+
a
−
2
and
g
(
x
)
=
[
2
+
sin
−
1
2
x
1
+
x
2
]
g(x) = \left[ 2 + \sin^{-1} \frac{2x}{1+x^2} \right]
g
(
x
)
=
[
2
+
sin
−
1
1
+
x
2
2
x
]
. If the set of real values of 'a' for which
f
(
g
(
x
)
)
<
0
,
∀
x
∈
R
f(g(x)) < 0, \forall x \in R
f
(
g
(
x
))
<
0
,
∀
x
∈
R
is
(
k
1
,
k
2
)
(k_1, k_2)
(
k
1
,
k
2
)
, then find the value of
(
10
k
1
−
3
k
2
)
(10k_1 - 3k_2)
(
10
k
1
−
3
k
2
)
. [Note :
[
k
]
[k]
[
k
]
denotes greatest integer less than or equal to
k
k
k
.]
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