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2019-IMOC
A1
Functional equation
Functional equation
Source: IMOC SL A1
December 15, 2019
algebra
functional equation
IMOC
Problem Statement
Find all functions
f
:
R
→
R
f:\mathbb{R}\to\mathbb{R}
f
:
R
→
R
such that for all
x
,
y
∈
R
x,y\in\mathbb{R}
x
,
y
∈
R
,
f
(
x
y
+
f
(
x
)
)
=
f
(
x
f
(
y
)
)
+
x
f(xy+f(x))=f(xf(y))+x
f
(
x
y
+
f
(
x
))
=
f
(
x
f
(
y
))
+
x
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