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April 13th, 2014, 11:59 AM  #1 
Senior Member Joined: Mar 2012 From: Belgium Posts: 654 Thanks: 11  power of 2 zero function
Find a function such that $\displaystyle f(2^n)=0$ for every $\displaystyle n \in Z$ and $\displaystyle f(x)=0$ is not correct.

April 13th, 2014, 01:13 PM  #2 
Global Moderator Joined: May 2007 Posts: 6,754 Thanks: 695  
April 13th, 2014, 01:59 PM  #3  
Math Team Joined: Dec 2006 From: Lexington, MA Posts: 3,267 Thanks: 408  Hello, gelatine1! I suppose we can create functions of the form: $\displaystyle f(x) \,=\,x  x$ Quote:
 
April 14th, 2014, 01:45 AM  #4 
Senior Member Joined: Mar 2012 From: Belgium Posts: 654 Thanks: 11 
I was thinking of $\displaystyle f(x) = 2^{\left \lfloor log(x) \right \rfloor}+2^{\left \lfloor log(x/2) \right \rfloor}  x$ where log is base 2 This is also a fractal function (I just call it like that ). Is this anything that exist ? I mean a fractal function ? 
April 14th, 2014, 03:18 AM  #5 
Senior Member Joined: Mar 2012 From: Belgium Posts: 654 Thanks: 11 
Whoops I meant $\displaystyle f(x) = 2^{\left \lfloor log(x) \right \rfloor}  x$

April 14th, 2014, 07:46 AM  #6 
Math Team Joined: Apr 2010 Posts: 2,780 Thanks: 361 
I don't understand what you want. What if x = 2^n? Then f(2^n) = 0 which isn't correct.


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