1. Not finding help here? Sign up for a free 30min tutor trial with Chegg Tutors
    Dismiss Notice
Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Confused about +- symbol use in inverse function

  1. Jun 20, 2012 #1
    1. The problem statement, all variables and given/known data



    2. Relevant equations



    3. The attempt at a solution

    Hi, so this isn't a question, it's just an example that they've given, but I don't understand the explanation given.


    You have :

    y = x^2 - 4
    x = y^2 - 4
    y^2 = x + 4
    y = ± sqrt(x+4)


    I don't get why there is a ± symbol there. My book says that it's necessary because there are two values for y that will satisfy the equation, and that if x = 0, y could be +2 or -2.


    I understand that y could = +2, because sqrt 4 = +2, but I don't see how it could equal -2.

    How would I know that I should include the ± symbol in front of the sqrt(x+4)? Thanks
     
  2. jcsd
  3. Jun 20, 2012 #2

    Ray Vickson

    User Avatar
    Science Advisor
    Homework Helper

    What is (-2)*(-2)?

    RGV
     
  4. Jun 20, 2012 #3
    Whenever you take the square root of something it requires a +or- because the square of either the negative or positive value of that term would yield the same number when it is squared. for instance (-x)^2=(x)^2

    since you are squaring y, you must be aware that the sqrt of (x+4) will net y regardless if it is positive or negative
     
  5. Jun 20, 2012 #4
    AHHHH! I get it.

    This forum rocks, thanks!
     
  6. Jun 20, 2012 #5
    indeed it does
     
  7. Jun 21, 2012 #6

    HallsofIvy

    User Avatar
    Staff Emeritus
    Science Advisor

    Note, by the way, that what this is saying is that the original function does NOT HAVE an inverse! A function has an inverse if and only if it is "one to one". That is, there is only one value of x that gives a specific y value. It that is not true, we can choose a specific one of the x values for a given y value, as here choosing "+" or "-", which is equivalent to choosing a subset of the original function.
     
  8. Jun 21, 2012 #7
    For example, if you have ##p^2=2##, then ##p=\pm\sqrt2##. Same thing here.
     
    Last edited: Jun 21, 2012
  9. Jun 21, 2012 #8
    ±√2 that is
     
  10. Jun 21, 2012 #9
    Oops, sorry about that. Editted.
     
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook




Similar Discussions: Confused about +- symbol use in inverse function
Loading...