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Soros Olympiad in Mathematics
I Soros Olympiad 1994-95 (Rus + Ukr)
10.6
f(x+2^y)=f(2^x)+f(y) (I Soros Olympiad 1994-95 R1 10.6 11.6)
f(x+2^y)=f(2^x)+f(y) (I Soros Olympiad 1994-95 R1 10.6 11.6)
Source:
July 31, 2021
algebra
functional equation
Problem Statement
Find all functions
f
:
R
ā
R
f:R\to R
f
:
R
ā
R
such that for any real
x
,
y
x, y
x
,
y
,
f
(
x
+
2
y
)
=
f
(
2
x
)
+
f
(
y
)
f(x+2^y)=f(2^x)+f(y)
f
(
x
+
2
y
)
=
f
(
2
x
)
+
f
(
y
)
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