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Byju's Answer
Standard XII
Mathematics
General Tips for Choosing Function
A function f ...
Question
A function f (x) satisfies the following property:f (xy)= flx) f(y). Show that the function f (x) is continuous forall values of x if it is continuous at x 1.
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Similar questions
Q.
A function
f
(
x
)
satisfies the following property:
f
(
x
⋅
y
)
=
f
(
x
)
f
(
y
)
. Show that the function
f
(
x
)
is continuous for all values of x if it is continuous at
x
=
1
.
Q.
A continuous real function
f
satisfies
f
(
2
x
)
=
3
f
(
x
)
∀
x
∈
R
. If
1
∫
0
f
(
x
)
d
x
=
1
, then the value of definite integral
2
∫
1
f
(
x
)
d
x
is
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.
lf
f
(
x
y
)
=
f
(
x
)
.
f
(
y
)
∀
x
,
y
∈
R
. lf the function is continuous at one point
x
=
a
, then
f
(
x
)
is:
Q.
If
f
:
R
→
R
is a continuous function and satisfies
f
(
x
)
=
e
x
+
1
∫
0
e
x
f
(
t
)
d
t
, then
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