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Math Help - give an example

  1. #1
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    give an example

    Give an example of a function  f: [0,1] \to R such that  f \in R[0,1] [i.e f is Riemann integrable over [0,1]] , f(x)>0, \ \forall x \in [0,1] , \ but \ \frac{1}{f}  is not in  R  [0,1]
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    Quote Originally Posted by flower3 View Post
    Give an example of a function  f: [0,1] \to R such that  f \in R[0,1] [i.e f is Riemann integrable over [0,1]] , f(x)>0, \ \forall x \in [0,1] , \ but \ \frac{1}{f} is not in  R [0,1]


    f(x)=\left\{\begin{array}{ll}1&\;\;if\,\,x=0\\x&\;  \;otherwise\end{array}\right.

    Tonio
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    MHF Contributor Drexel28's Avatar
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    Quote Originally Posted by flower3 View Post
    Give an example of a function  f: [0,1] \to R such that  f \in R[0,1] [i.e f is Riemann integrable over [0,1]] , f(x)>0, \ \forall x \in [0,1] , \ but \ \frac{1}{f}  is not in  R  [0,1]
    tonio's answer is of course great, but more generally all you need to do is find a function which has one discontinuity on [0,1] (guess where) such that it's multiplicative inverse is unbounded!
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