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# [Solved] Just a little math question

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### #1CryZe  Members   -  Reputation: 768

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Posted 05 September 2012 - 12:19 PM

I have a function:

and I need two functions g(x) and h(y) where the following is true:

I don't know if it's possible, but it would greatly improve the quality of my algorithm.

### #2Álvaro  Crossbones+   -  Reputation: 13649

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Posted 05 September 2012 - 12:27 PM

No, it cannot be done. The square root messes things up.

Consider this:
f(0,0) = 1
f(1,0) = e^-1
f(0,1) = e^-1

If g(x) and h(y) existed, you would have
g(0)*h(0) = 1
g(1)*h(0) = e^-1
g(0)*h(1) = e^-1
g(1)*h(1) = (g(1)*h(0)) * (g(0)*h(1)) / (g(0)*h(0)) = e^-2

But f(1,1) = e^-sqrt(2) instead.

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