Results 1 to 2 of 2

Math Help - FUNction

  1. #1
    Junior Member mathbuoy's Avatar
    Joined
    Nov 2008
    Posts
    28

    Exclamation FUNction

    Given that f(x^2 - 2) = x + (1 / x). Find f(x).

    *show working and explanation, PLS
    Follow Math Help Forum on Facebook and Google+

  2. #2
    Super Member
    earboth's Avatar
    Joined
    Jan 2006
    From
    Germany
    Posts
    5,829
    Thanks
    123
    Quote Originally Posted by mathbuoy View Post
    Given that f(x^2 - 2) = x + (1 / x). Find f(x).

    *show working and explanation, PLS
    1. You are supposed to know that f(f^{-1}(x))=f^{-1}(f(x))=x with f^{-1}(x) being the inverse of f(x).

    2. Calculate the inverse of

    y = x^2-2~\implies~x=y^2-2~\implies~y=\pm\sqrt{x+2}

    3. Use the new y-term as argument on the given function:

    f((\sqrt{x+2})^2-2)=\sqrt{x+2}+\dfrac1{\sqrt{x+2}}

    f(x)=\dfrac{(\sqrt{x+2})^2+1}{\sqrt{x+2}}=\dfrac{x  +3}{\sqrt{x+2}}
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Replies: 20
    Last Post: November 27th 2012, 05:28 AM
  2. Replies: 0
    Last Post: October 19th 2011, 04:49 AM
  3. Replies: 4
    Last Post: October 27th 2010, 05:41 AM
  4. Replies: 3
    Last Post: September 14th 2010, 02:46 PM
  5. Replies: 2
    Last Post: September 2nd 2010, 10:28 AM

Search Tags


/mathhelpforum @mathhelpforum