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Byju's Answer
Standard XII
Mathematics
General Tips for Choosing Function
For real numb...
Question
For real numbers x and y, the relation f satisfies f(xy) = f(x).f(y) and f(0)≠0. Find the value of f(2019).
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Similar questions
Q.
Let
f
:
[
0
,
1
]
→
R
be such that
f
(
x
y
)
=
f
(
x
)
.
f
(
y
)
for all x,y,
∈
[0,1], and
f
(
0
)
≠
0
. If
y
=
y
(
x
)
satisfies the differential equation ,
d
y
d
x
=
f
(
x
)
with
y
(
0
)
=
1
, then
y
(
1
4
)
+
y
(
3
4
)
is equal to
Q.
Find the natural number
a
for which
∑
n
k
=
1
f
(
a
+
k
)
=
16
(
2
n
−
1
)
where the function
f
satisfies the relation
f
(
x
+
y
)
=
f
(
x
)
.
f
(
y
)
for all natural numbers
x
,
y
and further
f
(
1
)
=
2
.
Q.
Let
f
be a function satisfying
f
(
x
y
)
=
f
(
x
)
y
for all positive real numbers
x
and
y
. If
f
(
30
)
=
20
, then the value of
f
(
40
)
is
Q.
Let
f
:
Z
→
Z
be a function satisfying
f
(
0
)
≠
0
,
f
(
1
)
=
0
and
f
(
x
y
)
+
f
(
x
)
f
(
y
)
=
f
(
x
)
+
f
(
y
)
;
(
f
(
x
−
y
)
−
f
(
0
)
)
f
(
x
)
f
(
y
)
=
0
,
for all
x
,
y
,
∈
Z
, simultaneously.
(a) Find the set of all possible values of the function
f
.
(b) If
f
(
10
)
≠
0
a
n
d
f
(
2
)
=
0
, find the set of all integers
n
such that
f
(
n
)
≠
0
.
Q.
Let
f
:
R
+
→
R
+
be a function satisfying the relation \(f(x.f(y))=f(xy)+x
~for~all~x,y \epsilon R^{+}\). Then
l
i
m
x
→
0
(
(
f
(
x
)
)
1
3
−
1
(
f
(
x
)
)
1
2
−
1
)
=
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