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KEAM 2017 Math Paper
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© examsnet.com
Question : 73
Total: 120
If
f
(
x
)
=
1
x
2
+
4
x
+
4
−
4
x
4
+
4
x
3
+
4
x
2
+
4
x
3
+
2
x
2
,
then
f
(
1
2
)
is equal to
1
2
-1
3
4
Validate
Solution:
We have,
f
(
x
)
=
1
x
2
+
4
x
+
4
−
4
x
4
+
4
x
3
+
4
x
2
+
4
x
3
+
2
x
2
=
1
(
x
+
2
)
2
−
4
x
2
(
x
+
2
)
2
+
4
x
2
(
x
+
2
)
=
x
2
−
4
+
4
(
x
+
2
)
(
x
+
2
)
2
⋅
x
2
=
x
2
−
4
+
4
x
+
8
(
x
+
2
)
2
⋅
x
2
=
x
2
+
4
x
+
4
(
x
+
2
)
2
⋅
x
2
=
(
x
+
2
)
2
(
x
+
2
)
2
⋅
x
2
=
1
x
2
∴
f
(
x
)
=
1
x
2
⇒
f
(
1
2
)
=
1
(
1
2
)
2
=
4
© examsnet.com
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