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Problem with squares and roots

  1. Apr 21, 2014 #1
    1. The problem statement, all variables and given/known data

    Hi, I am currently studying for a exam and I have noticed I have difficulty with squares and roots. I decided to take a problem from an exam so that I can illustrate the problems I am having with it.

    2. Relevant equations

    If f(x) = √(x+1)2 - √(x-1)2

    (a) f(x) = 2; (b) f(x) = 2x; (c) f(x) = 2√x; (d) none of (a)-(c).

    3. The attempt at a solution

    My first instict is to remove the squares and the roots so that f(x) = x+1 - (x-1) which in turn gives me the answer (a). This is incorrect. I am guessing it has to do with the fact that x is not defined to be ≥ 0. Any help?
     
  2. jcsd
  3. Apr 21, 2014 #2
    Remember √x2 = |x| and not simply x.Now rewrite f(x) .

    No.The domain of the function is R .
     
    Last edited: Apr 21, 2014
  4. Apr 21, 2014 #3
    f(x) = |x+1| - |x-1|

    I'm a bit slow, where do I take it from here?
     
  5. Apr 21, 2014 #4
    Good...

    Now the function will be defined differently in different regions.First consider x<-1

    What is the value of |x+1| when x<-1 ?
    What is the value of |x-1| when x<-1 ?
    What is the value of |x+1|-|x+1|when x<-1 ?
     
  6. Apr 21, 2014 #5
    Alright now I understand completely! Thank you very much!
     
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