Results 1 to 4 of 4

Thread: Inverse funciton

  1. #1
    Member
    Joined
    Sep 2009
    Posts
    98

    Inverse funciton

    The function f(x)= ax+b , f-1(x)=8x-3. Find a and b

    I would be very happy if you explained how to do it.

    Thank you
    Follow Math Help Forum on Facebook and Google+

  2. #2
    Member
    Joined
    May 2009
    From
    New Delhi
    Posts
    153
    Quote Originally Posted by Oasis1993 View Post
    The function f(x)= ax+b , f-1(x)=8x-3. Find a and b

    I would be very happy if you explained how to do it.

    Thank you
    let f(x)= ax+b =y (say)
    then ax+b =y  \quad \Rightarrow \quad x= \frac{(y-b)}{a}
    or\ x=\frac{1}{a}y-\frac{b}{a}
     \therefore f^{-1} (y)=\frac{1}{a}y-\frac{b}{a} \quad \Rightarrow \quad (\because f(x)=y , taking inverse both side )
     or\ \color {blue} f^{-1} (x)=\frac{1}{a}x-\frac{b}{a}................(1)
    but given f^{-1}(x)=8x-3................(2)
    on comparison eq(1) and (2)
     \frac{1}{a}=8 \quad \Rightarrow a= \frac{1}{8}
    and
     \frac{b}{a}=3 \quad \Rightarrow b=3a={3\over 8}
    Follow Math Help Forum on Facebook and Google+

  3. #3
    Member
    Joined
    Sep 2009
    Posts
    98
    Thank you very much!
    Follow Math Help Forum on Facebook and Google+

  4. #4
    MHF Contributor

    Joined
    Apr 2005
    Posts
    18,188
    Thanks
    2424
    Just to put in my oar: 8x- 3 says "first multiply x by 8 and then subtract 3".

    The "inverse" is the inverse of the original operarations ("divide by 8" rather than "multiply by 8" and "add 3" rather than "subtract 3") done in the opposite order.

    So the inverse of "first multiply x by 8 and then subtract 3" is "first add 3 to x and then divide by 8".

    f(x)= \frac{x+ 3}{8}= \frac{1}{8}x+ \frac{3}{8}
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Replies: 1
    Last Post: Oct 14th 2010, 06:37 PM
  2. Inverse of Funciton
    Posted in the Pre-Calculus Forum
    Replies: 1
    Last Post: Aug 8th 2009, 06:24 PM
  3. Replies: 1
    Last Post: Feb 11th 2009, 04:52 PM
  4. onto funciton
    Posted in the Calculus Forum
    Replies: 1
    Last Post: Dec 14th 2008, 08:51 AM
  5. Probability density funciton
    Posted in the Calculus Forum
    Replies: 0
    Last Post: Apr 1st 2008, 01:17 PM

Search Tags


/mathhelpforum @mathhelpforum