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Simon Marais Mathematical Competition
2024 Simon Marais Mathematical Competition
B2
B2
Part of
2024 Simon Marais Mathematical Competition
Problems
(1)
Continuous FE over reals, f(x)=(x+1)f(x^2) for x in R\{-1,1}
Source: SMMC 2024 B2
10/12/2024
Determine all continuous functions
f
:
R
∖
{
1
}
→
R
f : \mathbb{R} \setminus \{1\} \to \mathbb{R}
f
:
R
∖
{
1
}
→
R
that satisfy
f
(
x
)
=
(
x
+
1
)
f
(
x
2
)
,
f(x) = (x+1) f(x^2),
f
(
x
)
=
(
x
+
1
)
f
(
x
2
)
,
for all
x
∈
R
∖
{
−
1
,
1
}
x \in \mathbb{R} \setminus \{-1, 1\}
x
∈
R
∖
{
−
1
,
1
}
.
algebra