April 24th, 2014, 02:19 PM  #1 
Senior Member Joined: Nov 2013 Posts: 434 Thanks: 8  f(x)
f(x^2 +1)=x^4 +2x^2+1 find domain and rang of f 
April 24th, 2014, 03:46 PM  #2 
Global Moderator Joined: May 2007 Posts: 6,786 Thanks: 708 
It looks like f(x) = x^2. I am not sure what you want. 
April 24th, 2014, 05:11 PM  #3 
Math Team Joined: Dec 2013 From: Colombia Posts: 7,671 Thanks: 2651 Math Focus: Mainly analysis and algebra 
Well the domain would be $[1,+\infty)$ I suppose. The range would be the corresponding values of $f(x^2 + 1)$.

April 24th, 2014, 10:20 PM  #4 
Senior Member Joined: Apr 2014 From: Greater London, England, UK Posts: 320 Thanks: 156 Math Focus: Abstract algebra 
The function is $f(g(x))=x^4+2x^2+1$ where $g(x)=x^2+1$ and $f(x)=x^2$ so the domain and range are both $[1,\,\infty)$.

April 24th, 2014, 10:44 PM  #5 
Newbie Joined: Apr 2014 From: USA Posts: 8 Thanks: 2 
I think the domain is (infinity. +infinity) because x can take any value and range is [1, +infinity) 
April 24th, 2014, 10:49 PM  #6 
Senior Member Joined: Apr 2014 From: Greater London, England, UK Posts: 320 Thanks: 156 Math Focus: Abstract algebra  
April 24th, 2014, 11:03 PM  #7 
Newbie Joined: Apr 2014 From: USA Posts: 8 Thanks: 2 
Yes you are right. Thanks for correcting
