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Canadian Mathematical Olympiad Qualification Repechage
2016 Canadian Mathematical Olympiad Qualification
4
f(x + f(y)) + f(x - f(y)) = x
f(x + f(y)) + f(x - f(y)) = x
Source: Canada Repêchage 2016/4
June 19, 2016
algebra
functional equation
function
Problem Statement
Determine all functions
f
:
R
→
R
f: \mathbb{R} \rightarrow \mathbb{R}
f
:
R
→
R
such that
f
(
x
+
f
(
y
)
)
+
f
(
x
−
f
(
y
)
)
=
x
.
f(x + f(y)) + f(x - f(y)) = x.
f
(
x
+
f
(
y
))
+
f
(
x
−
f
(
y
))
=
x
.
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