can anyone tell me the solution with full explanation
Suppose f is a continuous realvalued function defined on the closed interval [0,1]. Which of the following must be true?
1. There is a constant C>0 such that f(x)f(y)<= C for all x and y in [0,1]
2. There is a constant D>0 such that f(x)f(y)<= 1 for all x and y in [0,1] that satisfy xy<=D
3. There is a constant E>0 such that f(x)f(y)<= Exy for all x and y in [0,1]
plz reply
GR9768 Q64

 Posts: 27
 Joined: Sun Oct 17, 2010 4:57 am
Re: GR9768 Q64
A continuous function on a compact set is bounded. If M is the bound, then C = 2M works for (1). For (2), you have to remember that a continuous function on a compact set is uniformly continuous. (3) isn't true: consider f(x) = x^(1/2).