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2012 Centers of Excellency of Suceava
2
Find function xf(x/a)-f(a/x)=b
Find function xf(x/a)-f(a/x)=b
Source:
October 31, 2019
function
Find all functions
algebra
Problem Statement
Find all functions
f
:
R
⟶
R
f:\mathbb{R}\longrightarrow\mathbb{R}
f
:
R
⟶
R
that verify, for any nonzero real number
x
x
x
the relation
x
f
(
x
/
a
)
−
f
(
a
/
x
)
=
b
,
xf(x/a)-f(a/x)=b,
x
f
(
x
/
a
)
−
f
(
a
/
x
)
=
b
,
where
a
≠
0
,
b
a\neq 0,b
a
=
0
,
b
are two real numbers. Dan Popescu
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