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KEAM 2018 Math Paper
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© examsnet.com
Question : 91
Total: 120
Let
f
:
(
−
1
,
1
)
→
(
−
1
,
1
)
be continuous,
f
(
x
)
=
f
(
x
2
)
for all
x
∊
(
−
1
,
1
)
and
f
(
0
)
=
1
12
,
then the value of
4
f
(
1
4
)
is
1
2
3
4
5
Validate
Solution:
∵
f
is continuous
∴
f
(
0
)
=
f
(
0
+
h
)
=
f
(
0
−
h
)
f
(
1
4
)
=
f
(
1
4
+
h
)
f
(
0
)
=
f
(
0
+
1
4
)
Given,
f
(
1
2
)
=
f
(
1
2
2
)
∴
f
(
0
)
=
f
(
0
+
1
2
2
)
=
1
2
....(i)
Therefore,
4
f
(
1
4
)
=
4
⋅
1
2
[using Eq. (i)]
=
2
© examsnet.com
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