MathDB
Problems
Contests
National and Regional Contests
Saudi Arabia Contests
Saudi Arabia BMO TST
2022 Saudi Arabia BMO + EGMO TST
p2
p2
Part of
2022 Saudi Arabia BMO + EGMO TST
Problems
(1)
f(g(x)) = x^3 and g(f(x)) = x^2.
Source: 2022 Saudi Arabia March Camp Test p2 BMO + EGMO TST
5/13/2024
Determine if there exist functions
f
,
g
:
R
→
R
f, g : R \to R
f
,
g
:
R
→
R
satisfying for every
x
∈
R
x \in R
x
∈
R
the following equations
f
(
g
(
x
)
)
=
x
3
f(g(x)) = x^3
f
(
g
(
x
))
=
x
3
and
g
(
f
(
x
)
)
=
x
2
g(f(x)) = x^2
g
(
f
(
x
))
=
x
2
.
algebra