KONWhat is the solution to the functional equation f(x,y)=g(r(x)+h(y))?

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SUMMARY

The functional equation f(x,y) = g(r(x) + h(y)) has a solution, as established in the discussion. By defining g(x) = x, r(x) = x, and h(x) = x, the equation simplifies to f(x,y) = x + y. To find a unique solution for f(x,y), it is essential to identify the appropriate functions r(x) and h(y) that satisfy the equation. This approach confirms that the functional equation can indeed be solved with the correct function definitions.

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let be the functional equation f(x,y)=g(r(x)+h(y)) my question is..does this equation have a solution?..thanks...
 
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Ofcourse,
let g(x) = x
r(x) = x
h(x) = x
then, f(x,y) = x + y
:p

Btw,
this is a functional equation.

-- AI
 


Yes, this functional equation does have a solution. In order to find the solution, we need to determine the functions r(x) and h(y) that are being added together inside the function g. Once we have these functions, we can plug them into the equation and find a unique solution for f(x,y). So, the solution to this functional equation would involve finding the appropriate functions r(x) and h(y) and then using them to determine the value of f(x,y).
 

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