MathDB
Problems
Contests
National and Regional Contests
Korea Contests
Korea National Olympiad
2015 Korea National Olympiad
1
Familiar Functional Equation
Familiar Functional Equation
Source: 2015 Korean Mathematical Olympiad P5
November 1, 2015
function
algebra
functional equation
Problem Statement
Find all functions
f
:
R
→
R
f: \mathbb{R} \rightarrow \mathbb{R}
f
:
R
→
R
such that for all reals
x
,
y
,
z
x,y,z
x
,
y
,
z
, we have
(
f
(
x
)
+
1
)
(
f
(
y
)
+
f
(
z
)
)
=
f
(
x
y
+
z
)
+
f
(
x
z
−
y
)
(f(x)+1)(f(y)+f(z))=f(xy+z)+f(xz-y)
(
f
(
x
)
+
1
)
(
f
(
y
)
+
f
(
z
))
=
f
(
x
y
+
z
)
+
f
(
x
z
−
y
)
Back to Problems
View on AoPS