The function
defined for all triples
of real numbers, is such that there are two functions
and
defined for all pairs of real numbers, such that
for all real numbers
and
Show that there is a function
of one real variable, such that
for all real numbers
and
%V0
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 $z.$
Školjka