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, 11:01 AMzannagorfeProving 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, 11:29 AMSpringFan25Re: Proving a function is wrong
if f(x) + g(y) = xy then $\displaystyle f(x) + f(x) = x^2$

so the only possible candidate for f(x) is $\displaystyle f(x) = 0.5 x^2$.

You can similarly reason for f(y) and hence end up with the (incorrect) equality $\displaystyle 0.5x^2 + 0.5y^2 = xy$, which you can easily show is false with a counter example.

You try part (b).