I'm trying to show that if f is continuous real-valued function on [a,b] satisfying integral from 1 to b (f(x)*g(x)) dx = 0 for every confinuous function g on [a,b] then f(x) = 0 for all x an element in [a,b]
What I tried is assuming that f(x) >= 0 for all x an element in [a,b] but I need help in breaking the cases and how many cases are there?