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Byju's Answer
Standard XII
Mathematics
Strictly Decreasing Functions
If f be decre...
Question
If f be decreasing continuous function satisfying
f
(
x
+
y
)
=
f
(
x
)
+
f
(
y
)
−
f
(
x
)
f
(
y
)
∀
x
,
y
∈
R
;
f
′
(
0
)
=
−
1
, then
∫
1
0
f
(
x
)
d
x
is
A
1
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B
1
−
e
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C
2
−
e
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D
n
o
n
e
o
f
t
h
e
s
e
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Solution
The correct option is
C
2
−
e
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0
Similar questions
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
Q.
If f is a differentiable function on R and
f
′
(
0
)
=
2
satisfying
f
(
x
+
y
)
=
f
(
x
)
+
f
(
y
)
1
−
f
(
x
)
f
(
y
)
then
f
(
π
/
8
)
is equal to
Q.
Let
f
be a continuous function satisfying
f
(
x
)
f
(
y
)
=
f
(
x
)
+
f
(
y
)
+
f
(
x
y
)
−
2
for all
x
,
y
∈
R
and
f
(
2
)
=
5
then
lim
x
→
4
f
(
x
)
is
Q.
A function
f
:
R
→
R
+
satisfies
f
(
x
+
y
)
=
f
(
x
)
f
(
y
)
∀
x
,
y
ϵ
R
.
If
f
′
(
0
)
=
2
then
∀
x
,
y
ϵ
R
,
f
′
(
x
)
=
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
1
f
′′
(
2
)
is
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