
PreCalculus PreCalculus Math Forum 
 LinkBack  Thread Tools  Display Modes 
July 13th, 2017, 12:47 PM  #1 
Newbie Joined: Sep 2014 From: Morocco Posts: 29 Thanks: 0  Generalizing with a function
Hi, I'm given the function defined as follows, with c a real that's strictly positive. For each x in IR, $\displaystyle f(x) = \frac{x}{\sqrt{1+cx^{2}}}$. The exercise is to calculate the image of f(x), then the image of the former image, then lastly, to generalize. This is what I have managed to do, and I'd like to have an idea on how I can formalize a generalization. $\displaystyle f(f(x)) = f(x)\frac{1}{\sqrt{1+cf(x)^{2}}}$ $\displaystyle f(f(f(x))) = f(x)\frac{1}{\sqrt{1+cf(f(x))^{2}}}$ Thanks a lot. 
July 13th, 2017, 12:59 PM  #2  
Senior Member Joined: Aug 2012 Posts: 1,414 Thanks: 342  Quote:
On a notational note. IR is the worst of all possible display options for $\mathbb R$. You can see how I did that by quoting my post. Other alternatives are boldface R, or copy/paste from the excellent math.typeit.org. Or just say "the reals."  
July 16th, 2017, 12:16 PM  #3 
Newbie Joined: Sep 2014 From: Morocco Posts: 29 Thanks: 0 
Hi Maschke, thanks for the reply. I think what is required is to deduce a general formula based on those two results. I found this exercise under a text about induction. Thanks again. 
July 16th, 2017, 12:33 PM  #4 
Member Joined: Oct 2009 Posts: 97 Thanks: 33  Correct, they want you to find a general formula. For that, you use your expressoin $f(f(x))$ and you substitute $f(x)$ in there with your function value, then you simplify. It's a bit of nasty algebra.


Tags 
function, generalizing 
Thread Tools  
Display Modes  

Similar Threads  
Thread  Thread Starter  Forum  Replies  Last Post 
guessing the base function of a real function that meets certain requirements  vlekje5  PreCalculus  11  March 27th, 2017 12:58 PM 
Limit generalizing  MisaKr  Calculus  2  October 24th, 2016 11:13 AM 
Generalizing the prime number theorem. Sorta.  standardmalpractice  Math  1  March 21st, 2016 08:47 AM 
Derivation of tau function, sigma, euler and mobius function  msgelyn  Number Theory  2  January 12th, 2014 03:13 AM 
Generalizing a recursive series  boyo  Applied Math  1  November 20th, 2009 08:39 AM 