Help Solving Integral Inequality: f to 1/f

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The discussion revolves around the integrability of the function 1/f given that f is integrable and bounded below. Participants highlight that the assertion is false, using the example of f(x) = x on the interval [0,1] to illustrate the point. Clarification is requested regarding the conditions under which the inequality might hold, specifically if f is strictly positive and bounded away from zero. The conversation emphasizes the importance of accurately stating the problem to facilitate assistance. Ultimately, the conclusion is that the original claim cannot be supported as presented.
shegiggles
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I really need help on this. Completely lost. Please help me.
Let f: [a,b] -> R. Given f is integrable and bounded below, show 1/f is integrable.
 
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It's not true. What about f(x)=x on [0,1]?
 
Well, perhaps he meant that 0<|f|<k, on [0,1] for some constant k?
 
Erm, arildno, you should reread that. (k=1...).
 
matt grime said:
Erm, arildno, you should reread that. (k=1...).

can you please help me with this problem?
Thanks
 
We can't because we have shown the question to be false.
 
It would help if you would state exactly what the problem is. It cannot be what you originally wrote!
 

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