MathDB
Problems
Contests
National and Regional Contests
Taiwan Contests
TST Round 2
2020 Taiwan TST Round 2
1
1
Part of
2020 Taiwan TST Round 2
Problems
(1)
Another simple functional equation
Source: 2020 Taiwan TST Round 2 Independent study 2-1
5/23/2020
Let
R
\mathbb{R}
R
denote the set of all real numbers. Determine all functions
f
:
R
ā
R
f:\mathbb{R}\to\mathbb{R}
f
:
R
ā
R
such that for all real numbers
x
x
x
and
y
y
y
,
f
(
x
y
+
x
f
(
x
)
)
=
f
(
x
)
(
f
(
x
)
+
f
(
y
)
)
.
f(xy+xf(x))=f(x)\left(f(x)+f(y)\right).
f
(
x
y
+
x
f
(
x
))
=
f
(
x
)
(
f
(
x
)
+
f
(
y
)
)
.
function
algebra
functional equation
Taiwan