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UPSEE 2017 Solved Paper
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© examsnet.com
Question : 142
Total: 150
Let
f
be an odd function defined on the real number such that
f
(
x
)
=
3
sin
x
+
4
cos
x
, for
x
≥
0
, then
f
(
x
)
for
x
<
0
is
−
3
sin
x
+
4
cos
x
−
3
sin
x
−
4
cos
x
3
sin
x
+
4
cos
x
3
sin
x
−
4
cos
x
Validate
Solution:
Given,
f
(
x
)
=
3
sin
x
+
4
cos
x
When,
x
<
0
∴
−
x
>
0
∴
f
(
−
x
)
=
3
sin
(
−
x
)
+
4
cos
(
−
x
)
......(i)
But,
f
(
x
)
is odd function
∴
f
(
−
x
)
=
−
f
(
x
)
, when
x
<
0
⇒
f
(
x
)
=
−
f
(
−
x
)
=
−
[
3
sin
(
−
x
)
+
4
cos
(
−
x
)
]
[
From Eq. (i)]
=
3
sin
x
−
4
cos
x
© examsnet.com
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