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Istek Lyceum Math Olympiad 2016
1
Functional Equation
Functional Equation
Source:
October 31, 2015
function
algebra
functional equation
Istek Lyceum MO
Problem Statement
Find all functions
f
:
R
→
R
f:\mathbb{R}\to\mathbb{R}
f
:
R
→
R
for which
f
(
x
+
y
)
=
f
(
x
−
y
)
+
f
(
f
(
1
−
x
y
)
)
f(x+y)=f(x-y)+f(f(1-xy))
f
(
x
+
y
)
=
f
(
x
−
y
)
+
f
(
f
(
1
−
x
y
))
holds for all real numbers
x
x
x
and
y
y
y
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