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

Printable View

- September 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 - September 23rd 2012, 11:29 AMSpringFan25Re: 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).