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Standard XII
Maths
Question
Determine whether the following is even or odd
f
(
x
)
=
log
(
x
+
√
1
+
x
2
)
f
(
x
)
is even function
f
(
x
)
is neither even nor odd
f
(
x
)
is odd function
f
(
x
)
is periodic function
A
f
(
x
)
is neither even nor odd
B
f
(
x
)
is periodic function
C
f
(
x
)
is even function
D
f
(
x
)
is odd function
Open in App
Solution
Verified by Toppr
f
(
x
)
=
log
(
x
+
√
1
+
x
2
)
f
(
−
x
)
=
log
(
−
x
+
√
1
+
x
2
)
f
(
x
)
+
f
(
−
x
)
=
log
(
(
x
+
√
1
+
x
2
)
(
−
x
+
√
1
+
x
2
)
)
=
log
(
1
+
x
2
−
x
2
)
=
log
(
1
)
=
0
Hence,
f
(
x
)
is odd.
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4
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