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MathLinks Contest 4th
3.2
0432 functional 4th edition Round 3 p2
0432 functional 4th edition Round 3 p2
Source:
May 7, 2021
algebra
functional equation
4th edition
Problem Statement
Determine all functions
f
:
R
→
R
f : R \to R
f
:
R
→
R
such that
f
(
x
)
≥
0
f(x) \ge 0
f
(
x
)
≥
0
for all positive reals
x
x
x
,
f
(
0
)
=
0
f(0) = 0
f
(
0
)
=
0
and for all reals
x
,
y
x, y
x
,
y
f
(
x
+
y
−
x
y
)
=
f
(
x
)
+
f
(
y
)
−
f
(
x
y
)
.
f(x + y -xy) = f(x) + f(y) - f(xy).
f
(
x
+
y
−
x
y
)
=
f
(
x
)
+
f
(
y
)
−
f
(
x
y
)
.
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