MathDB
Problems
Contests
National and Regional Contests
Switzerland Contests
Switzerland Team Selection Test
1999 Switzerland Team Selection Test
3
1/x f(-x)+ f(/x)= x
1/x f(-x)+ f(/x)= x
Source: Switzerland - Swiss TST 1999 p3
February 19, 2020
functional equation
functional
algebra
Problem Statement
Find all functions
f
:
R
−
{
0
}
→
R
f : R -\{0\} \to R
f
:
R
−
{
0
}
→
R
that satisfy
1
x
f
(
−
x
)
+
f
(
1
x
)
=
x
\frac{1}{x}f(-x)+ f\left(\frac{1}{x}\right)= x
x
1
f
(
−
x
)
+
f
(
x
1
)
=
x
for all
x
≠
0
x \ne 0
x
=
0
.
Back to Problems
View on AoPS