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3
Continuous f(x-f(x))=x/2 does not exist
Continuous f(x-f(x))=x/2 does not exist
Source: Turkey TST 2001 - P6
April 4, 2013
function
algebra proposed
algebra
Problem Statement
Show that there is no continuous function
f
:
R
→
R
f:\mathbb{R}\rightarrow \mathbb{R}
f
:
R
→
R
such that for every real number
x
x
x
f
(
x
−
f
(
x
)
)
=
x
2
.
f(x-f(x)) = \dfrac x2.
f
(
x
−
f
(
x
))
=
2
x
.
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