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Best way to find range

  1. Sep 10, 2008 #1
    1. The problem statement, all variables and given/known data

    find range for f(x) = sqrt of x-1

    f(x) 1/x^2-1

    2. Relevant equations


    3. The attempt at a solution

    well, i know this is dumb to ask, but i am very very curious...

    let say the first one, sqrt of x-1
    if we want to find the range, obviously, you can tell just by looking at the function, since it is sqrt, it has to be y>0

    second function, f(x)= 1/x^2-1
    so i tried to use use the x-y method, you replace x with y, and y with x

    so it becomes x = 1/y^2-1
    now it is my range, but if i want to know the notation interval, like ( infinite, 0), then how do i solve for the range and get some actual indications for the range.
  2. jcsd
  3. Sep 10, 2008 #2


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    Science Advisor
    Homework Helper

    Your first and best bet is to draw a graph of each function. Try doing that. Find critical points, the whole bit. And when you post, try and make the nature of the function clear. 1/x^2-1 could mean either (1/x^2)-1 or 1/(x^2-1). I think you mean the latter. And I think your range for the first one should be y>=0 (i.e. include y=0).
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