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Standard XII
Mathematics
Question
If
f
(
x
)
=
1
2
(
3
x
+
3
−
x
)
,
g
(
x
)
=
1
2
(
3
x
−
3
−
x
)
then
f
(
x
)
g
(
y
)
+
f
(
y
)
g
(
x
)
is equal to
f
(
x
+
y
)
g
(
x
+
y
)
2
f
(
x
)
2
g
(
x
)
A
g
(
x
+
y
)
B
2
g
(
x
)
C
f
(
x
+
y
)
D
2
f
(
x
)
Open in App
Solution
Verified by Toppr
⇒
f
(
x
)
g
(
y
)
=
1
4
(
3
x
+
3
−
x
)
(
3
y
−
3
−
y
)
⇒
1
4
(
3
x
+
y
+
3
y
−
x
−
3
x
−
y
−
3
−
x
−
y
)
⇒
f
(
y
)
g
(
x
)
=
1
4
(
3
x
+
y
−
3
y
−
x
+
3
x
−
y
−
3
−
x
−
y
)
⇒
f
(
x
)
g
(
y
)
+
f
(
y
)
g
(
x
)
=
1
4
×
2
(
3
x
+
y
−
3
−
x
−
y
)
⇒
1
2
(
3
x
+
y
−
3
−
(
x
+
y
)
)
⇒
g
(
x
+
y
)
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Similar Questions
Q1
If
f
(
x
)
=
1
2
(
3
x
+
3
−
x
)
,
g
(
x
)
=
1
2
(
3
x
−
3
−
x
)
then
f
(
x
)
g
(
y
)
+
f
(
y
)
g
(
x
)
is equal to
View Solution
Q2
The value
∫
x
sin
−
1
x
d
x
=
x
2
2
f
(
x
)
+
1
2
[
x
2
g
(
x
)
+
1
2
f
(
x
)
]
−
1
2
f
(
x
)
+
C
then
f
(
x
)
and
g
(
x
)
are :
View Solution
Q3
Let
f
(
x
)
=
3
x
−
2
−
1
x
+
3
and
g
(
x
)
=
x
2
−
4
x
+
19
x
2
+
x
−
6
. If
f
(
x
)
=
g
(
x
)
, then
x
=
View Solution
Q4
If
f
(
x
)
=
2
x
−
3
,
g
(
x
)
=
x
−
3
x
+
4
and
h
(
x
)
=
−
2
(
2
x
+
1
)
x
2
+
x
−
12
, then
lim
x
→
3
[
f
(
x
)
+
g
(
x
)
+
h
(
x
)
]
is
View Solution
Q5
If
f
(
x
)
=
2
x
−
3
,
g
(
x
)
=
x
−
3
x
+
4
and
h
(
x
)
=
−
2
(
2
x
+
1
)
x
2
+
x
−
12
, then
lim
x
→
3
[
f
(
x
)
+
g
(
x
)
+
h
(
x
)
]
is equal to:
View Solution