Results 1 to 4 of 4
Like Tree3Thanks
  • 1 Post By Soroban
  • 1 Post By HallsofIvy
  • 1 Post By letranger9000

Math Help - Is the reciprocal of f (x) = (2x+1) / (x-3) -> F^-1 (x) = (3x+1) / (x-2) ?

  1. #1
    Newbie
    Joined
    Oct 2013
    From
    canada
    Posts
    3
    Thanks
    1

    Is the reciprocal of f (x) = (2x+1) / (x-3) -> F^-1 (x) = (3x+1) / (x-2) ?

    I don't have access to a teacher in the present moment, I just want to make sure I understand right. If I am wrong please point out where is my error, thank you.

    f (x) = (2x+1) / (x-3)

    y=(2x+1) / (x-3)

    x=(2y+1) / (y-3)

    x(y-3)=(2y+1)

    xy-3x-2y=1

    xy-2y=(3x+1)

    y(x-2)=(3x+1)

    y(x-2)/(x-2)=(3x+1)/(x-2)

    y=(3x+1)/(x-2)
    Follow Math Help Forum on Facebook and Google+

  2. #2
    Super Member

    Joined
    May 2006
    From
    Lexington, MA (USA)
    Posts
    11,738
    Thanks
    644

    Re: Is the reciprocal of f (x) = (2x+1) / (x-3) -> F^-1 (x) = (3x+1) / (x-2) ?

    Hello, letranger9000!

    You don't mean "reciprocal" . . . You mean "inverse".


    f(x) \;=\;\frac{2x+1}{x-3}

    y\;=\;\frac{2x+1}{x-3}

    x\;=\;\frac{2y+1}{y-3}

    x(y-3) \;=\;(2y+1)

    xy-3x \;=\;2y+1

    xy-2y \;=\;3x+1

    y(x-2)\;=\;3x+1

    y\;=\;\frac{3x+1}{x-2}

    Good work!
    Punchline: / f^{\text{-}1}(x) \;=\;\frac{3x+1}{x-2}


    Do you know how to check your answer?

    Evaluate f\left(f^{-1}(x)\right) or f^{-1}\big(f(x)\big).
    Either must simplify to x.

    f\left(f^{-1}(x)\right) \;=\;\frac{2\left(\frac{3x+1}{x-2}\right) + 1}{\left(\frac{3x+1}{x-2}\right) - 3}

    Multiply by \tfrac{x-2}{x-2}\!:\;\frac{2(3x+1) + (x-2)}{(3x+1) - 3(x-2)} \;=\;\frac{6x+2 + x - 2}{3x+1-3x+6} \;=\;\frac{7x }{7} \;=\;x

    ta-DAA!
    Thanks from letranger9000
    Follow Math Help Forum on Facebook and Google+

  3. #3
    MHF Contributor

    Joined
    Apr 2005
    Posts
    15,693
    Thanks
    1466

    Re: Is the reciprocal of f (x) = (2x+1) / (x-3) -> F^-1 (x) = (3x+1) / (x-2) ?

    Be careful of your terminolgy. The reciprocal of \dfrac{3x+ 1}{x- 3} is \dfrac{x- 3}{3x+ 1}.

    But the inverse function is f^{-1}(x)= \dfrac{3x+1}{x- 2} as you have.
    Thanks from letranger9000
    Follow Math Help Forum on Facebook and Google+

  4. #4
    Newbie
    Joined
    Oct 2013
    From
    canada
    Posts
    3
    Thanks
    1

    Re: Is the reciprocal of f (x) = (2x+1) / (x-3) -> F^-1 (x) = (3x+1) / (x-2) ?

    Thanks guys, appreciated. And yes I meant inverse, although in french an "inverse" is a "reciprocal", hence the source of my confusion.
    Thanks from topsquark
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. reciprocal sum
    Posted in the Algebra Forum
    Replies: 1
    Last Post: February 6th 2013, 09:03 AM
  2. reciprocal
    Posted in the Math Topics Forum
    Replies: 2
    Last Post: February 5th 2010, 09:11 AM
  3. reciprocal cm?
    Posted in the Calculus Forum
    Replies: 2
    Last Post: November 2nd 2009, 01:54 AM
  4. reciprocal
    Posted in the Algebra Forum
    Replies: 1
    Last Post: September 22nd 2008, 03:47 PM
  5. If the reciprocal of x+1 is...
    Posted in the Algebra Forum
    Replies: 1
    Last Post: February 21st 2007, 04:39 PM

Search Tags


/mathhelpforum @mathhelpforum