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JEE Advanced Model Paper 4 with solutions for online practice
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© examsnet.com
Question : 50
Total: 54
Consider the function f(x) =
[
c
o
s
(
t
a
n
−
1
(
s
i
n
(
c
o
t
−
1
x
)
)
)
]
2
. Which of thefollowing is correct?
Range of f is (0,1)
f is even
f'(0) = 0
The line y = 1 is asymptode to the graph y = f ( x)
Validate
Solution:
Domain is x ∊ R
Also f(x) =
[
c
o
s
(
t
a
n
−
1
(
s
i
n
(
c
o
t
−
1
x
)
)
)
]
2
where cotθ = x
=
[
c
o
s
(
t
a
n
−
1
(
1
√
1
+
x
2
)
)
]
2
=
(
c
o
s
ϕ
)
2
where tan
ϕ
=
1
√
1
+
x
2
=
(
√
1
+
x
2
√
2
+
x
2
)
2
g(x) =
1
+
x
2
2
+
x
2
= 1 -
1
2
+
x
2
Range is
[
1
2
,
1
)
; f'(x) =
2
x
(
2
+
x
2
)
2
Hence f'(0) = 0
Also
l
i
m
x
→
∞
f(x) = 1
Hence (b) , (c) , (d)
© examsnet.com
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