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National and Regional Contests
Netherlands Contests
Dutch BxMO/EGMO TST
2013 Dutch BxMO/EGMO TST
4
4
Part of
2013 Dutch BxMO/EGMO TST
Problems
(1)
Functional equation.
Source: Netherlands BxMO/EGMO Team Selection Test-2013
5/9/2017
Determine all functions
f
:
R
→
R
f:\mathbb{R}\to\mathbb{R}
f
:
R
→
R
satisfying
f
(
x
+
y
f
(
x
)
)
=
f
(
x
f
(
y
)
)
−
x
+
f
(
y
+
f
(
x
)
)
f(x+yf(x))=f(xf(y))-x+f(y+f(x))
f
(
x
+
y
f
(
x
))
=
f
(
x
f
(
y
))
−
x
+
f
(
y
+
f
(
x
))
functional equation
Determine all functions
TST
algebra