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Latvia Contests
Latvia BW TST
2016 Latvia Baltic Way TST
4
4
Part of
2016 Latvia Baltic Way TST
Problems
(1)
f(2^x+2y)=2^y f(f(x)) f(y)
Source: 2016 Latvia BW TST P4
12/17/2022
Find all functions
f
:
R
ā
R
f : R \to R
f
:
R
ā
R
defined for real numbers, take real values and for all real
x
x
x
and
y
y
y
the equality holds:
f
(
2
x
+
2
y
)
=
2
y
f
(
f
(
x
)
)
f
(
y
)
.
f(2^x+2y) =2^yf(f(x))f(y).
f
(
2
x
+
2
y
)
=
2
y
f
(
f
(
x
))
f
(
y
)
.
algebra
functional
functional equation