Help Solving Integral Inequality: f to 1/f

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    Inequality Integral
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SUMMARY

The discussion centers on the integrability of the function 1/f, where f is a bounded and integrable function defined on the interval [a, b]. Participants clarify that the statement is false, particularly using the example f(x) = x on [0, 1], which leads to 1/f being non-integrable at x = 0. The condition that 0 < |f| < k for some constant k is suggested as a necessary requirement for the integrability of 1/f, highlighting the importance of precise definitions in mathematical discussions.

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  • Understanding of integrable functions in real analysis
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  • Familiarity with the concept of limits and continuity
  • Basic grasp of inequalities and their implications in calculus
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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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