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All-Russian Olympiad Regional Round
1999 All-Russian Olympiad Regional Round
11.1
11.1
Part of
1999 All-Russian Olympiad Regional Round
Problems
(1)
f(x)+f(ax) is continuous - All-Russian MO 1999 Regional (R4) 11.1
Source:
9/25/2024
The function
f
(
x
)
f(x)
f
(
x
)
, defined on the entire real line, is known but that for any
a
>
1
a > 1
a
>
1
the function
f
(
x
)
+
f
(
a
x
)
f(x)+f(ax)
f
(
x
)
+
f
(
a
x
)
is continuous on the entire line. Prove that
f
(
x
)
f(x)
f
(
x
)
is also continuous along the entire line.
algebra
continuous
function