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Baltic Way
2011 Baltic Way
5
Determine f(0) if given f(f(x))
Determine f(0) if given f(f(x))
Source: Baltic Way 2011
November 6, 2011
function
algebra proposed
algebra
Problem Statement
Let
f
:
R
→
R
f:\mathbb{R}\to\mathbb{R}
f
:
R
→
R
be a function such that
f
(
f
(
x
)
)
=
x
2
−
x
+
1
f(f(x))=x^2-x+1
f
(
f
(
x
))
=
x
2
−
x
+
1
for all real numbers
x
x
x
. Determine
f
(
0
)
f(0)
f
(
0
)
.
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