MathDB
Problems
Contests
National and Regional Contests
PEN Problems
PEN K Problems
18
18
Part of
PEN K Problems
Problems
(1)
K 18
Source:
5/25/2007
Find all functions
f
:
Q
→
R
f: \mathbb{Q}\to \mathbb{R}
f
:
Q
→
R
such that for all
x
,
y
∈
Q
x,y\in \mathbb{Q}
x
,
y
∈
Q
:
f
(
x
y
)
=
f
(
x
)
f
(
y
)
−
f
(
x
+
y
)
+
1.
f(xy)=f(x)f(y)-f(x+y)+1.
f
(
x
y
)
=
f
(
x
)
f
(
y
)
−
f
(
x
+
y
)
+
1.
function
induction
Functional Equations