Results 1 to 2 of 2

Thread: inverse of a piecewise function

  1. #1
    Member
    Joined
    Nov 2010
    Posts
    93

    inverse of a piecewise function

    Hi, if I have a piecewise function such as:

    f(x) = (x-1)^2 if x>1
    or tan(x) if -π/2 < x < 0

    If I want want to find the inverse, do I simply calculate the inverse for each of piecewise operations ?
    eg. (x-1)^2 has the inverse y = 1 +- sqrt(x)
    and tan(x) has the inverse tan^-1(x)

    is it is straightforward as that or I am missing something ?
    thanks for any help.
    Follow Math Help Forum on Facebook and Google+

  2. #2
    MHF Contributor
    skeeter's Avatar
    Joined
    Jun 2008
    From
    North Texas
    Posts
    16,216
    Thanks
    3702

    Re: inverse of a piecewise function

    Quote Originally Posted by fran1942 View Post
    Hi, if I have a piecewise function such as:

    f(x) = (x-1)^2 if x>1
    or tan(x) if -π/2 < x < 0

    If I want want to find the inverse, do I simply calculate the inverse for each of piecewise operations ?
    eg. (x-1)^2 has the inverse y = 1 +- sqrt(x)
    and tan(x) has the inverse tan^-1(x)

    is it is straightforward as that or I am missing something ?
    the restriction placed on the domain of the original function will be the range of the inverse function ...

    for $\displaystyle f(x) = (x-1)^2$ , $\displaystyle x > 1$ ; $\displaystyle f^{-1}(x) = 1 + \sqrt{x}$ , $\displaystyle x > 0$

    (note: why is $\displaystyle 1 - \sqrt{x}$ not used?)

    for $\displaystyle f(x) = \tan{x}$ , $\displaystyle -\frac{\pi}{2} < x < 0$ ; $\displaystyle f^{-1}(x) = \tan^{-1}{x}$ , $\displaystyle x < 0$
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Replies: 14
    Last Post: Oct 7th 2011, 09:45 PM
  2. Piecewise function
    Posted in the Calculus Forum
    Replies: 2
    Last Post: Nov 17th 2010, 10:51 AM
  3. Replies: 3
    Last Post: Jun 4th 2010, 10:40 PM
  4. Piecewise function
    Posted in the Pre-Calculus Forum
    Replies: 0
    Last Post: Sep 11th 2009, 10:19 PM
  5. Piecewise function
    Posted in the LaTeX Help Forum
    Replies: 4
    Last Post: Dec 16th 2008, 10:43 AM

Search tags for this page

Search Tags


/mathhelpforum @mathhelpforum