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Problems
Contests
National and Regional Contests
Switzerland Contests
Switzerland Team Selection Test
2004 Switzerland Team Selection Test
11
11
Part of
2004 Switzerland Team Selection Test
Problems
(1)
f((x+y)/(x-y) )= (f(x)+ f(y))/(f(x)- f(y)) , injective
Source: Switzerland - Swiss TST 2004 p11
2/18/2020
Find all injective functions
f
:
R
→
R
f : R \to R
f
:
R
→
R
such that for all real
x
≠
y
x \ne y
x
=
y
,
f
(
x
+
y
x
−
y
)
=
f
(
x
)
+
f
(
y
)
f
(
x
)
−
f
(
y
)
f\left(\frac{x+y}{x-y}\right) = \frac{f(x)+ f(y)}{f(x)- f(y)}
f
(
x
−
y
x
+
y
)
=
f
(
x
)
−
f
(
y
)
f
(
x
)
+
f
(
y
)
functional equation
functional