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Contests
National and Regional Contests
Latvia Contests
Latvia BW TST
2015 Latvia Baltic Way TST
2
2
Part of
2015 Latvia Baltic Way TST
Problems
(1)
f(2x - f (x)) = x, f(x) > x, f(x) > f(y) for all real x > y
Source: 2015 Latvia BW TST P2
12/16/2022
It is known about the function
f
:
R
→
R
f : R \to R
f
:
R
→
R
that
∙
\bullet
∙
f
(
x
)
>
f
(
y
)
f(x) > f(y)
f
(
x
)
>
f
(
y
)
for all real
x
>
y
x > y
x
>
y
∙
\bullet
∙
f
(
x
)
>
x
f(x) > x
f
(
x
)
>
x
for all real
x
x
x
∙
\bullet
∙
f
(
2
x
−
f
(
x
)
)
=
x
f(2x - f (x)) = x
f
(
2
x
−
f
(
x
))
=
x
for all real
x
x
x
. Prove that
f
(
x
)
=
x
+
f
(
0
)
f(x) = x + f(0)
f
(
x
)
=
x
+
f
(
0
)
for all real numbers
x
x
x
.
functional equation
functional
algebra