MathDB

Functional equation

Source: APMO 1989

March 10, 2006

functioninductioncalculusderivativelimitalgebrarecursion

Problem Statement

Determine all functions

f

from the reals to the reals for which (1)

f(x)

is strictly increasing and (2)

f(x) + g(x) = 2x

for all real

x

, where

g(x)

is the composition inverse function to

f(x)

. (Note:

f

and

g

are said to be composition inverses if

f(g(x)) = x

and

g(f(x)) = x

for all real

x

.)

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