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Byju's Answer
Standard XII
Mathematics
Log Function
Match the fol...
Question
Match the following functions satisfying particular functional relationship
Column-I
(A)
f
(
x
+
y
)
=
f
(
x
)
+
f
(
y
)
(B)
f
(
x
y
)
=
f
(
x
)
+
f
(
y
)
(C)
f
(
x
+
y
)
=
f
(
x
)
⋅
f
(
y
)
(D)
f
(
X
)
+
f
(
y
)
=
f
(
x
+
y
1
−
x
y
)
Column-II
(p)
log
3
x
(q)
t
a
n
−
1
x
(r)
3
x
(s)
3
x
(t)
A transcendental function
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Solution
(A)
3
(
x
+
y
)
=
3
x
+
3
y
⇒
f
(
x
+
y
)
=
f
(
x
)
+
f
(
y
)
(B)
log
3
x
y
=
log
3
x
+
log
3
y
⇒
f
(
x
y
)
=
f
(
x
)
+
f
(
y
)
(C)
f
(
x
+
y
)
=
f
(
x
)
⋅
f
(
y
)
⇒
3
x
+
y
=
3
x
+
3
y
(D)
tan
−
1
x
+
tan
−
1
y
=
tan
−
1
(
x
+
y
1
−
x
y
)
⇒
f
(
x
)
+
f
(
y
)
=
f
(
x
+
y
1
−
x
y
)
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0
Similar questions
Q.
Consider a continuous function and differentiable function
′
f
′
satisfies the functional equation
f
(
x
)
+
f
(
y
)
=
f
(
x
+
y
+
x
y
)
+
x
y
for
x
,
y
>
−
1
and
f
′
(
0
)
=
0
,then
The value of
f
(
e
−
1
)
is
Q.
Assume
f
is differentiable function satisfying
f
(
x
+
y
)
=
f
(
x
)
+
f
(
y
)
+
x
y
and
lim
h
→
0
f
(
h
)
h
=
3
then
f
(
1
)
equals
Q.
Let a function
f
:
R
→
R
satisfy the equation
f
(
x
+
y
)
=
f
(
x
)
+
f
(
y
)
for all
x
,
y
. If the function
f
(
x
)
is continuous at
x
=
0
, then
Q.
Let
f
:
R
→
R
be a differentiable function satisfying
f
(
x
+
y
)
=
f
(
x
)
+
f
(
y
)
+
x
y
for all
x
,
y
∈
R
and
lim
h
→
0
1
h
f
(
h
)
=
3.
Which of the following statements is (are) CORRECT?
Q.
If f be decreasing continuous function satisfying
f
(
x
+
y
)
=
f
(
x
)
+
f
(
y
)
−
f
(
x
)
f
(
y
)
∀
x ,y
∈
R
;
f
(
0
)
≠
0
, then
∫
1
0
f
(
x
)
d
x
is
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