
PreCalculus PreCalculus Math Forum 
 LinkBack  Thread Tools  Display Modes 
October 22nd, 2017, 03:44 AM  #1 
Newbie Joined: Oct 2017 From: canada Posts: 3 Thanks: 0  Why 3,5 can't be a part of domain? Untitled.png Within given equation, you can change this to 4/(x/31). which I think the answer should be All Real Numbers? since X isn't taking any part from denominators 
October 22nd, 2017, 07:53 AM  #2 
Global Moderator Joined: Oct 2008 From: London, Ontario, Canada  The Forest City Posts: 7,642 Thanks: 960 Math Focus: Elementary mathematics and beyond 
What about x = 0? What about x = 3?

October 22nd, 2017, 10:47 AM  #3 
Global Moderator Joined: Dec 2006 Posts: 18,166 Thanks: 1425 
For $x \ne 0$, $h(x) = \dfrac{4x}{3  x}$, so the discontinuity at $x = 0$ is removable.

November 8th, 2017, 05:38 AM  #4  
Math Team Joined: Jan 2015 From: Alabama Posts: 2,829 Thanks: 753  Quote: The domain of the initial $\displaystyle \frac{4}{\frac{3}{x} 1}$ is "all real numbers except x= 0 or x= 3". The domain of $\displaystyle \frac{4}{\frac{x}{3} 1}$ is "all real numbers except 3" but that is not equivalent to the original fraction. Quote:
 
November 8th, 2017, 05:59 PM  #5 
Senior Member Joined: May 2016 From: USA Posts: 826 Thanks: 335 
Yes, you can say that $h(x) = \dfrac{4}{\dfrac{3}{x}  1} = \dfrac{4x}{3  x} = g(x) \text { if } x \ne 0 \text { and } x \ne 3.$ But if x = 0, you do not have a definition for h(x) so you cannot say that it equals g(0). And of course neither g(x) nor h(x) is defined if x = 3 so saying h(3) = g(3) is meaningless for two distinct reasons. 
November 8th, 2017, 07:17 PM  #6  
Senior Member Joined: Aug 2012 Posts: 1,641 Thanks: 415  Quote:  

Tags 
domain, part 
Thread Tools  
Display Modes  

Similar Threads  
Thread  Thread Starter  Forum  Replies  Last Post 
Determine the domain and the against domain of the following function  kanchinha123  PreCalculus  2  April 26th, 2017 10:25 PM 
New concept  part quantum part surface across the world  for data and nanotech  BenFRayfield  Physics  0  March 14th, 2015 07:20 PM 
Minimum Real Part theorem issue on RHP (unbounded domain)  aleberto69  Complex Analysis  2  October 12th, 2013 02:27 AM 
Find the Domain of the function part 2  Shamieh  Algebra  4  July 3rd, 2013 07:30 PM 
Integration over open domain or close domain  good_phy  Calculus  1  October 12th, 2008 10:26 AM 