Expert: Paul Klarreich - 12/14/2008

Question
I am having a hard time on this analysis hw question:

Suppose that f is integrable on the interval [a,b] and there exists a k>0 such that f(x) > = k for all x exists on interval [a,b]. Prove that 1/f is integrable on [a,b].

i know that f is bounded, but I really am stuck on how to do this.

Answer
Questioner:   Megan
Category:  Advanced Math
Private:  No
 
Subject:  Analysis Hw
Question:  I am having a hard time on this analysis hw question:

Suppose that f is integrable on the interval [a,b] and there exists a k>0 such that f(x) > = k for all x exists on interval [a,b]. Prove that 1/f is integrable on [a,b].

i know that f is bounded, but I really am stuck on how to do this.
....................................
Hi, Megan,

If  f(x) >= k > 0 on [a,b], then wouldn't it be true that

1/f(x) <= 1/k on [a,b], so 1/f(x) is bounded.  {If f(x) >= k > 0, then surely f(x) > 0 and so is 1/f(x).}

Does this help?