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Quandaries & Queries
Q & Q
 Topic: functional
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 A function satisfying f(x) + 2f(1/x) = x 2008-03-25 From Joan:Let f be a function satisfying f(x) + 2f(1/x) =x for all real numbers (x does not equal 0) a) Find f(1) justify your answer b) Find f(2) justify your answerAnswered by Penny Nom. The limit of a rational function 2007-05-28 From Imad:     3 _______ 3 _______ lim \/ 1 + x -    \/ 1 - x x->0 ---- ----------------------------               xAnswered by Penny Nom. A functional equation 2002-10-14 From Rob:Let f be a function whose domain is a set of all positive integers and whose range is a subset of the set of all positive integers with these conditions: a) f(n+1)>f(n) b) f(f(n))=3(n) Answered by Claude Tardif. Dual spaces 2001-11-26 From Hoda: In the book "Linear Functional Analysis" from Epstein there is a proof (page 116) of the following theorem: The dual space of Lp is equal to Lq. Later, it is stated as a theorem without proof that for 1 <= p < +infinite, The dual space of lp is equal to lq. Answered by Doug Farenick. A Functional Equation. 1997-02-26 From Ronald Lui:Find all functions f:S --> S statisfying the two conditions: 1)f(x+f(y)+xf(y))=y+f(x)+yf(x) for all x and y in S 2)f(x)/x is strictly increasing on each of the interval -1Answered by Saroop Kaul and Chris Fisher.

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