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JEE Advanced 2016 Paper 2 Mathematics Q10
Mathematics
Problem
Let
f
:
[
−
1
2
,
2
]
→
R
f:\left[-\frac12,2\right]\to\mathbb R
f
:
[
−
2
1
,
2
]
→
R
and
g
:
[
−
1
2
,
2
]
→
R
g:\left[-\frac12,2\right]\to\mathbb R
g
:
[
−
2
1
,
2
]
→
R
be functions defined by
f
(
x
)
=
[
x
2
−
3
]
f(x)=[x^2-3]
f
(
x
)
=
[
x
2
−
3
]
and
g
(
x
)
=
∣
x
∣
f
(
x
)
+
∣
4
x
−
7
∣
f
(
x
)
g(x)=|x|f(x)+|4x-7|f(x)
g
(
x
)
=
∣
x
∣
f
(
x
)
+
∣4
x
−
7∣
f
(
x
)
, where
[
y
]
[y]
[
y
]
denotes the greatest integer less than or equal to
y
y
y
for
y
∈
R
y\in\mathbb R
y
∈
R
. Then
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