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Korea Junior Mathematics Olympiad
2008 Korea Junior Math Olympiad
7
7
Part of
2008 Korea Junior Math Olympiad
Problems
(1)
f(x + y) = g (1/x+1/y) (xy)^{2008} , xy\ne 0 , find f,g:R -> R
Source: KJMO 2008 p7
5/2/2019
Find all pairs of functions
f
;
g
:
R
→
R
f; g : R \to R
f
;
g
:
R
→
R
such that for all reals
x
.
y
≠
0
x.y \ne 0
x
.
y
=
0
:
f
(
x
+
y
)
=
g
(
1
x
+
1
y
)
⋅
(
x
y
)
2008
f(x + y) = g \left(\frac{1}{x}+\frac{1}{y}\right) \cdot (xy)^{2008}
f
(
x
+
y
)
=
g
(
x
1
+
y
1
)
⋅
(
x
y
)
2008
algebra
functional equation
functions