MathDB
Problems
Contests
National and Regional Contests
USA Contests
USA - College-Hosted Events
MMATHS problems
2019 MMATHS
4
4
Part of
2019 MMATHS
Problems
(1)
2019 MMATHS Tiebreaker p4 - c^2f(x + y) = f(x)f(y), continuous f
Source:
10/7/2023
The continuous function
f
(
x
)
f(x)
f
(
x
)
satisfies
c
2
f
(
x
+
y
)
=
f
(
x
)
f
(
y
)
c^2f(x + y) = f(x)f(y)
c
2
f
(
x
+
y
)
=
f
(
x
)
f
(
y
)
for all real numbers
x
x
x
and
y
,
y,
y
,
where
c
>
0
c > 0
c
>
0
is a constant. If
f
(
1
)
=
c
f(1) = c
f
(
1
)
=
c
, find
f
(
x
)
f(x)
f
(
x
)
(with proof).
functional equation
algebra