MathDB

The function

\varphi(x,y,z)

defined for all triples

(x,y,z)

of real numbers, is such that there are two functions

f

and

g

defined for all pairs of real numbers, such that

\varphi(x,y,z) = f(x+y,z) = g(x,y+z)

for all real numbers

x,y

and

z.

Show that there is a function

h

of one real variable, such that

\varphi(x,y,z) = h(x+y+z)

for all real numbers

x,y

and

z.

Problem Statement