Thread: Proving 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!

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).