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UPSC NDA Math Model Paper 2
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© examsnet.com
Question : 8
Total: 120
The function
f
(
x
)
=
log
(
x
+
√
x
2
+
1
)
is:
An even function.
An odd function.
A periodic function.
Neither an even nor an odd function.
Validate
Solution:
We have
f
(
x
)
=
log
(
x
+
√
x
2
+
1
)
⇒
f
(
−
x
)
=
log
(
−
x
+
√
x
2
+
1
)
Now,
f
(
x
)
+
f
(
−
x
)
=
log
(
x
+
√
x
2
+
1
)
+
log
(
−
x
+
√
x
2
+
1
)
=
log
[
(
x
+
√
x
2
+
1
)
(
−
x
+
√
x
2
+
1
)
]
=
log
[
(
√
x
2
+
1
)
2
−
x
2
]
=
log
1
=
0
⇒
f
(
−
x
)
=
−
f
(
x
)
∴ f(x) is an odd function.
© examsnet.com
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