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Bulgaria Team Selection Test
2005 Bulgaria Team Selection Test
3
3
Part of
2005 Bulgaria Team Selection Test
Problems
(1)
Functional Equation
Source: Bulgarian IMO TST 2005, Day 1, Problem 3
7/7/2013
Let
R
∗
\mathbb{R}^{*}
R
∗
be the set of non-zero real numbers. Find all functions
f
:
R
∗
→
R
∗
f : \mathbb{R}^{*} \to \mathbb{R}^{*}
f
:
R
∗
→
R
∗
such that
f
(
x
2
+
y
)
=
(
f
(
x
)
)
2
+
f
(
x
y
)
f
(
x
)
f(x^{2}+y) = (f(x))^{2} + \frac{f(xy)}{f(x)}
f
(
x
2
+
y
)
=
(
f
(
x
)
)
2
+
f
(
x
)
f
(
x
y
)
, for all
x
,
y
∈
R
∗
x,y \in \mathbb{R}^{*}
x
,
y
∈
R
∗
and
−
x
2
≠
y
-x^{2} \not= y
−
x
2
=
y
.
function
algebra proposed
algebra