







A function satisfying f(x) + 2f(1/x) = x 
20080325 

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 answer Answered by Penny Nom. 





The limit of a rational function 
20070528 

From Imad: 3 _______ 3 _______
lim \/ 1 + x  \/ 1  x
x>0  
x Answered by Penny Nom. 





A functional equation 
20021014 

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 
20011126 

From Hoda: In the book "Linear Functional Analysis" from Epstein there is a proof (page 116) of the following theorem: The dual space of L^{p} is equal to L^{q}. Later, it is stated as a theorem without proof that for 1 <= p < +infinite, The dual space of l^{p} is equal to l^{q}. Answered by Doug Farenick. 





A Functional Equation. 
19970226 

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 1 Answered by Saroop Kaul and Chris Fisher. 

