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JEE Advanced 2014 Paper 1
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© examsnet.com
Question : 50
Total: 60
Let
f
:
(
−
π
2
,
π
2
)
→
ℝ
be give by
f
(
x
)
=
(
log
(
sec
x
+
tan
x
)
)
3
.Then
f(x) is an odd function
f(x) is a one -one function
f(x) is an onto function
f(x) is an even function
Validate
Solution:
f
(
x
)
=
(
l
o
g
(
s
e
c
x
+
t
a
n
x
)
)
3
∀
x
∊
(
−
π
2
,
π
2
)
f
(
−
x
)
=
−
f
(
x
)
,hence
f
(
x
)
is an odd function
let
g
(
x
)
=
s
e
c
x
+
t
a
n
x
∀
x
∊
(
−
π
2
,
π
2
)
⇒
g
′
(
x
)
=
s
e
c
x
(
s
e
c
x
+
t
a
n
x
)
>
0
∀
x
∊
(
−
π
2
,
π
2
)
⇒
g
(
x
)
is one-one function
Hence
(
l
o
g
e
(
g
(
x
)
)
)
3
s one-one function
and
g
(
x
)
∊
(
0
,
∞
)
∀
x
∊
(
−
π
2
,
π
2
)
⇒
l
o
g
(
g
(
x
)
)
∊
R
Hence
f
(
x
)
is an onto function
© examsnet.com
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