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All-Russian Olympiad Regional Round
1997 All-Russian Olympiad Regional Round
11.8
f(a(x + y)) = f(x) + f(y) - All-Russian MO 1997 Regional (R4) 11.8
f(a(x + y)) = f(x) + f(y) - All-Russian MO 1997 Regional (R4) 11.8
Source:
September 24, 2024
algebra
functional
functional equation
Problem Statement
For which
a
a
a
, there is a function
f
:
R
ā
R
f: R \to R
f
:
R
ā
R
, different from a constant, such that
f
(
a
(
x
+
y
)
)
=
f
(
x
)
+
f
(
y
)
?
f(a(x + y)) = f(x) + f(y) ?
f
(
a
(
x
+
y
))
=
f
(
x
)
+
f
(
y
)?
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