Analysis 2 HELP!

1. Apr 6, 2008

Misswfish

Suppose f is continuous function on [a,b] such that for each continuous function g, $$\int$$(fg)dj = 0 (Note: integral is from a to b) , then f(x) = 0 for each x in [a,b].

I know that I should use the theorem If is continuous on [a,b], f(x)$$\geq$$0 for each x in [a,b] and theree is a number p i n [a,b] such that f(p) > 0, THen $$\int$$f dj > 0.

I just dont understand how they tie together.

2. Apr 6, 2008

slider142

What is the contrapositive of this statement? It pretty much falls out of it.

3. Apr 6, 2008

Misswfish

Ahhh my teacher told me to pick a "clever" g(x) so that we can use this theorem and therefore f(x) = 0. I was thinking contradiction but my teacher shot that down