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EAMCET Engineering 2002 Solved Paper
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© examsnet.com
Question : 163
Total: 200
The function
f
:
R
→
R
is defined by
f
(
x
)
=
cos
2
x
+
s
i
n
4
x
for
x
∈
R
, then
f
(
R
)
is equal to
(
3
4
,
1
]
[
3
4
,
1
)
[
3
4
,
1
]
(
3
4
,
1
)
Validate
Solution:
We have,
f
(
x
)
=
cos
2
x
+
s
i
n
4
x
=
1
−
s
i
n
2
x
+
s
i
n
4
x
=
1
−
s
i
n
2
x
(
1
−
s
i
n
2
x
)
=
1
−
s
i
n
2
x
cos
2
x
=
1
−
1
4
s
i
n
2
2
x
Here,
0
≤
s
i
n
2
2
x
≤
1
⇒
0
≤
s
i
n
2
2
x
4
≤
1
4
⇒
0
≥
−
s
i
n
2
2
x
4
≥
−
1
4
⇒
1
≥
1
−
s
i
n
2
2
x
4
≥
−
1
4
1
≥
1
−
s
i
n
2
2
x
4
≥
−
1
4
+
1
⇒
1
≥
1
−
s
i
n
2
2
x
4
≥
3
4
Range of
f
=
[
3
4
,
1
]
© examsnet.com
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