Results 1 to 5 of 5

Math Help - Find the Inverse?

  1. #1
    Junior Member
    Joined
    Sep 2009
    Posts
    32

    Find the Inverse?

    Hello, I've been trying to figure out how to solve this function but I keep getting stuck. The question asks:

    Find a formula for the inverse of the function:

    y = e^x / 1+5e^x

    My teacher said to substitute the variable p to replace e^x to make the function easier to solve.

    y = p / 1+5p^2

    I'm not really sure how to go about solving this question. Would I multiply all sides by the denominator to get rid of it and then somehow solve from there?

    Help is appreciated, so thanks in advance.
    Follow Math Help Forum on Facebook and Google+

  2. #2
    Master Of Puppets
    pickslides's Avatar
    Joined
    Sep 2008
    From
    Melbourne
    Posts
    5,236
    Thanks
    29
    Quote Originally Posted by dark-ryder341 View Post

    y = e^x / 1+5e^x

    My teacher said to substitute the variable p to replace e^x to make the function easier to solve.

    y = p / 1+5p^2
    How did you arrive at p^2 ?


    What is the original function?

    y = \frac{e^x}{ 1+5e^x}

    or

    y = \frac{e^x}{ 1}+5e^x
    Follow Math Help Forum on Facebook and Google+

  3. #3
    Junior Member
    Joined
    Sep 2009
    Posts
    32
    Oops, my mistake. I meant to write y = p / 1+5p

    The p is just a substitution for e^x

    The original function is:



    Thanks.
    Follow Math Help Forum on Facebook and Google+

  4. #4
    Flow Master
    mr fantastic's Avatar
    Joined
    Dec 2007
    From
    Zeitgeist
    Posts
    16,948
    Thanks
    5
    Quote Originally Posted by dark-ryder341 View Post
    Oops, my mistake. I meant to write y = p / 1+5p

    The p is just a substitution for e^x

    The original function is:



    Thanks.
    The inverse is given by y = f^{-1}(x) where x = \frac{e^y}{1 + 5 e^y}.

    Your job is to make y the subject. Let p = e^y:

    x = \frac{p}{1 + 5p} \Rightarrow x (1 + 5p) = p \Rightarrow x + 5px = p \Rightarrow x = p - 5px

    \Rightarrow x = p(1 - 5x) \Rightarrow p = \frac{x}{1 - 5x}.

    Substitute back for p and solve for y.
    Follow Math Help Forum on Facebook and Google+

  5. #5
    Junior Member
    Joined
    Sep 2009
    Posts
    32
    Thanks so much. It makes a lot of sense now.

    So now, substituting e^y back in, I get

    e^y = x / 1-5x

    If I take the ln of both sides:

    lne^y = ln (x/1-5x)

    lne^y = y...therefore

    y = ln (x/1-5x)
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Find the INverse
    Posted in the Number Theory Forum
    Replies: 2
    Last Post: March 9th 2010, 11:06 PM
  2. find the inverse
    Posted in the Calculus Forum
    Replies: 4
    Last Post: November 22nd 2009, 12:50 PM
  3. Find the inverse of F(x)?
    Posted in the Pre-Calculus Forum
    Replies: 5
    Last Post: September 10th 2009, 04:47 PM
  4. Find the Inverse
    Posted in the Pre-Calculus Forum
    Replies: 2
    Last Post: November 8th 2008, 10:14 PM
  5. Need to find Inverse of...
    Posted in the Calculus Forum
    Replies: 3
    Last Post: April 20th 2008, 05:01 PM

Search Tags


/mathhelpforum @mathhelpforum