MathDB
Problems
Contests
Undergraduate contests
IMC
1999 IMC
4
functional equation
functional equation
Source: IMC 1999 day 1 problem 4
November 19, 2005
function
real analysis
real analysis unsolved
Problem Statement
Find all strictly monotonic functions
f
:
R
+
→
R
+
f: \mathbb{R}^+\rightarrow\mathbb{R}^+
f
:
R
+
→
R
+
for which
f
(
x
2
f
(
x
)
)
=
x
f\left(\frac{x^2}{f(x)}\right)=x
f
(
f
(
x
)
x
2
)
=
x
for all
x
x
x
.
Back to Problems
View on AoPS