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Brazil Undergrad MO
2021 Brazil Undergrad MO
Problem 2
Problem 2
Part of
2021 Brazil Undergrad MO
Problems
(1)
f(x)^2=f(x sqrt(2))
Source: Brazilian Undergrad MO 2021 Problem 2
5/12/2022
Find all functions
f
:
R
→
R
f: \mathbb{R} \rightarrow \mathbb{R}
f
:
R
→
R
from
C
2
C^2
C
2
(id est,
f
f
f
is twice differentiable and
f
′
′
f''
f
′′
is continuous.) such that for every real number
t
t
t
we have
f
(
t
)
2
=
f
(
t
2
)
f(t)^2=f(t \sqrt{2})
f
(
t
)
2
=
f
(
t
2
)
.
functions
real analysis
function
Brazilian Undergrad MO 2021