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 $\displaystyle f(x) + f(x) = x^2$
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).