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Bundeswettbewerb Mathematik
1977 Bundeswettbewerb Mathematik
4
All functions f with f(x)+f(1- 1/x)=x
All functions f with f(x)+f(1- 1/x)=x
Source:
June 5, 2007
algebra unsolved
algebra
Problem Statement
Find all functions
f
:
R
→
R
f : \mathbb R \to \mathbb R
f
:
R
→
R
such that
f
(
x
)
+
f
(
1
−
1
x
)
=
x
,
f(x)+f\left(1-\frac{1}{x}\right)=x,
f
(
x
)
+
f
(
1
−
x
1
)
=
x
,
holds for all real
x
x
x
.
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