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1977 IMO Longlists
24
24
Part of
1977 IMO Longlists
Problems
(1)
Find all functions (something like tangents) - [ILL 1971]
Source:
1/11/2011
Determine all real functions
f
(
x
)
f(x)
f
(
x
)
that are defined and continuous on the interval
(
−
1
,
1
)
(-1, 1)
(
−
1
,
1
)
and that satisfy the functional equation
f
(
x
+
y
)
=
f
(
x
)
+
f
(
y
)
1
−
f
(
x
)
f
(
y
)
(
x
,
y
,
x
+
y
∈
(
−
1
,
1
)
)
.
f(x+y)=\frac{f(x)+f(y)}{1-f(x) f(y)} \qquad (x, y, x + y \in (-1, 1)).
f
(
x
+
y
)
=
1
−
f
(
x
)
f
(
y
)
f
(
x
)
+
f
(
y
)
(
x
,
y
,
x
+
y
∈
(
−
1
,
1
))
.
function
algebra
functional equation
algebra proposed