Results 1 to 10 of 10

Math Help - Composite Functions

  1. #1
    Newbie
    Joined
    Nov 2008
    Posts
    23

    Composite Functions

    I know this is really simple, but can someone help?

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

    find (f o f)(x)

    Thanks!!
    Follow Math Help Forum on Facebook and Google+

  2. #2
    A riddle wrapped in an enigma
    masters's Avatar
    Joined
    Jan 2008
    From
    Big Stone Gap, Virginia
    Posts
    2,551
    Thanks
    12
    Awards
    1
    Quote Originally Posted by rtwilton View Post
    I know this is really simple, but can someone help?

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

    find (f o f)(x)

    Thanks!!
    Is this your function: f(x)=x+\frac{1}{x}-1?

    Or is it this: f(x)=\frac{x+1}{x-1}?
    Follow Math Help Forum on Facebook and Google+

  3. #3
    Newbie
    Joined
    Nov 2008
    Posts
    23
    The lower function is mine! Sorry, forgot the brackets!
    Follow Math Help Forum on Facebook and Google+

  4. #4
    A riddle wrapped in an enigma
    masters's Avatar
    Joined
    Jan 2008
    From
    Big Stone Gap, Virginia
    Posts
    2,551
    Thanks
    12
    Awards
    1
    Quote Originally Posted by masters View Post
    f(x)=\frac{x+1}{x-1}?
    [f\circ f](x)=f[f(x)]

    f\left(\frac{x+1}{x-1}\right)=\frac{\frac{x+1}{x-1}+1}{\frac{x+1}{x-1}-1}

    Can you simplify?
    Follow Math Help Forum on Facebook and Google+

  5. #5
    Newbie
    Joined
    Nov 2008
    Posts
    23
    Wow, I knew it was simple, thanks so much, so basically it simplifies down to -1, correct?
    Follow Math Help Forum on Facebook and Google+

  6. #6
    A riddle wrapped in an enigma
    masters's Avatar
    Joined
    Jan 2008
    From
    Big Stone Gap, Virginia
    Posts
    2,551
    Thanks
    12
    Awards
    1
    Quote Originally Posted by rtwilton View Post
    Wow, I knew it was simple, thanks so much, so basically it simplifies down to -1, correct?
    I get something different. Can you show your work?
    Follow Math Help Forum on Facebook and Google+

  7. #7
    Newbie
    Joined
    Nov 2008
    Posts
    23
    Hmm I guess I thought that the fractions in the numerator and denominator would just cancel, but as I test my theory I see that does not work. I can hack away at it a little longer. . .
    Follow Math Help Forum on Facebook and Google+

  8. #8
    A riddle wrapped in an enigma
    masters's Avatar
    Joined
    Jan 2008
    From
    Big Stone Gap, Virginia
    Posts
    2,551
    Thanks
    12
    Awards
    1
    Quote Originally Posted by rtwilton View Post
    Hmm I guess I thought that the fractions in the numerator and denominator would just cancel, but as I test my theory I see that does not work. I can hack away at it a little longer. . .
    You are right. You cannot cancel over addition or subtraction. Here's a start:

    f\left(\frac{x+1}{x-1}\right)=\frac{\dfrac{x+1}{x-1}+1}{\dfrac{x+1}{x-1}-1}=\frac{\dfrac{x+1+x-1}{x-1}}{\dfrac{x+1-(x-1)}{x-1}}=\frac{\dfrac{2x}{x-1}}{\dfrac{2}{x-1}}=
    Last edited by masters; November 19th 2008 at 11:34 AM.
    Follow Math Help Forum on Facebook and Google+

  9. #9
    Newbie
    Joined
    Nov 2008
    Posts
    23
    Alright I am going to look at your work a little bit, run some errands, and come back to it. I think (hope) I can get it from here. I'll post and work/solution I have, thanks so much for everything!
    Follow Math Help Forum on Facebook and Google+

  10. #10
    Super Member

    Joined
    May 2006
    From
    Lexington, MA (USA)
    Posts
    11,658
    Thanks
    598
    Hello, rtwilton

    f(x) \:= \:\frac{x+1}{x-1}

    Find: . (f\circ f)(x)

    (f\circ f)(x) \;=\;f(f(x)) \;=\;f\left(\frac{x+1}{x-1}\right) \;=\;\frac{\dfrac{x+1}{x-1} + 1}{\dfrac{x+1}{x-1} - 1}

    Multiply by \frac{x-1}{x-1}\!:\quad\frac{(x-1)\left(\dfrac{x+1}{x-1} + 1\right)} {(x-1)\left(\dfrac{x+1}{x-1} - 1\right)} \;=\;\frac{(x+1) + (x-1)}{(x+1) - (x-1)} \;=\;\frac{2x}{2} \;=\;\boxed{ x}


    Note: This means that f(x) is its own inverse!

    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Composite functions.
    Posted in the Pre-Calculus Forum
    Replies: 2
    Last Post: October 16th 2011, 09:44 AM
  2. Composite Functions
    Posted in the Pre-Calculus Forum
    Replies: 1
    Last Post: April 26th 2010, 04:22 AM
  3. Composite functions
    Posted in the Algebra Forum
    Replies: 5
    Last Post: February 11th 2010, 11:00 AM
  4. Composite functions
    Posted in the Pre-Calculus Forum
    Replies: 10
    Last Post: December 8th 2007, 01:07 AM
  5. Composite functions
    Posted in the Pre-Calculus Forum
    Replies: 3
    Last Post: July 25th 2007, 10:06 PM

Search Tags


/mathhelpforum @mathhelpforum