Thread: Bounded functions ..

Hello
small question:

if f and g are bounded function then so is f+g and f-g

but what about fg and f/g ?
Are they will be bounded also?

If you know that |f(x)| <= C and |g(x)| <= C, then it is easy to find an upper bound on |f(x) * g(x)|.

On the other hand, f(x) / g(x) can be very large even if |g(x)| <= 1. In fact, in this case |f(x) / g(x)| can be made arbitrarily large by keeping f(x) constant and changing g(x) a little (by no more than 1).

Originally Posted by Liverpool

Hello
small question:

if f and g are bounded function then so is f+g and f-g

but what about fg and f/g ?
Are they will be bounded also?

If f is bounded by ±M, and g is bounded by ±N, then certainly it's true that fg is bounded by ±MN.

For f/g: what if g → 0 somewhere in its domain, and f = 1 at that same location?

Thanks!