I'm new to the forum but hope to contribute when and where I can.
I'm doing some study at the moment and I was stuck on the following problem.
Let the solution set of f(x)=0 be A and the solution set of g(x)=0 be B (here f and g are real functions taking real values).
What is the solution sets of f(x)g(x)=0 and of f(x)2+g(x)2=0.
I'm not sure how this answer is supposed to look.
My initial thoughts were something along the lines of
f(x).g(x) = A.B = 0 [A product B]
f(x)^2 + g(x)^2 = A^2 + B^2 = 0
But I really don't know if this is going in the right direction at all?
If you have a minute I would be grateful for your thoughts.