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KEAM 2012 Math Paper
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© examsnet.com
Question : 22
Total: 120
The range of the function
f
(
x
)
=
x
2
+
8
x
2
+
4
,
x
∊
R
is
[
−
1
,
3
2
]
(
1
,
2
]
(
1
,
2
)
[
1
,
2
]
[
3
2
,
2
]
Validate
Solution:
Let
y
=
f
(
x
)
=
x
2
+
8
x
2
+
4
⇒
x
2
(
y
−
1
)
+
4
y
=
8
⇒
x
2
=
8
−
4
y
y
−
1
⇒
x
=
√
8
−
4
y
y
−
1
since,
x
is real.
∴
y
−
1
>
0
and
8
−
4
y
≥
0
⇒
y
>
1
and
y
≤
2
∴
y
∈
(
1
,
2
]
© examsnet.com
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