How do i prove that these two functions DO NOT exist?

a) f(x) + g(y) = xy

b) f(x)g(y) = x+ y

Thanks so much! :D

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- Sep 23rd 2012, 12:01 PMzannagorfeProving a function is wrong
How do i prove that these two functions DO NOT exist?

a) f(x) + g(y) = xy

b) f(x)g(y) = x+ y

Thanks so much! :D - Sep 23rd 2012, 12:29 PMSpringFan25Re: Proving a function is wrong
if f(x) + g(y) = xy then

so the only possible candidate for f(x) is .

You can similarly reason for f(y) and hence end up with the (incorrect) equality , which you can easily show is false with a counter example.

You try part (b).