Results 1 to 4 of 4

Math Help - inverse

  1. #1
    Member
    Joined
    Nov 2005
    Posts
    172

    inverse

    dont know how to start this:

     f(x) = 5 + 5 x + 4 e^x

    find  f^{-1}(9) = ____
    Follow Math Help Forum on Facebook and Google+

  2. #2
    is up to his old tricks again! Jhevon's Avatar
    Joined
    Feb 2007
    From
    New York, USA
    Posts
    11,663
    Thanks
    3
    Quote Originally Posted by viet View Post
    dont know how to start this:

     f(x) = 5 + 5 x + 4 e^x

    find  f^{-1}(9) = ____
    There is a theorem that says:

    Let f be a one-to-one continuous function on an open interval I. If f is differentiable at x_0 \in I and if f'(x_0) \neq 0, then f^{-1} is differentiable at y_0 = f(x_0) and

    \left( f^{-1} \right)^{ \prime} (y_0) = \frac {1}{f'(x_0)}

    Note here, that f(0) = 9

    Let x_0 = 0 and y_0 = f(0) = 9

    Then \left( f^{-1} \right)^{ \prime} (9) = \frac {1}{f'(0)}

    Now continue
    Follow Math Help Forum on Facebook and Google+

  3. #3
    Grand Panjandrum
    Joined
    Nov 2005
    From
    someplace
    Posts
    14,972
    Thanks
    4
    Quote Originally Posted by viet View Post
    dont know how to start this:

     f(x) = 5 + 5 x + 4 e^x

    find  f^{-1}(9) = ____
    f(x) is an increasing function so if there is a solution to:

    f(x)=9

    it is unique. Now f(0)=9, so f^{-1}(9) = 0

    RonL
    Follow Math Help Forum on Facebook and Google+

  4. #4
    is up to his old tricks again! Jhevon's Avatar
    Joined
    Feb 2007
    From
    New York, USA
    Posts
    11,663
    Thanks
    3
    Quote Originally Posted by CaptainBlack View Post
    f(x) is an increasing function so if there is a solution to:

    f(x)=9

    it is unique. Now f(0)=9, so f^{-1}(9) = 0

    RonL
    well that was simple enough. anyway, my theorem is bound to come in handy at some point in the future
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. left inverse equivalent to inverse
    Posted in the Advanced Algebra Forum
    Replies: 1
    Last Post: June 30th 2011, 03:58 PM
  2. Inverse tan and inverse of tanh
    Posted in the Calculus Forum
    Replies: 2
    Last Post: October 31st 2010, 06:20 AM
  3. secant inverse in terms of cosine inverse?
    Posted in the Trigonometry Forum
    Replies: 1
    Last Post: August 30th 2010, 08:08 PM
  4. Replies: 1
    Last Post: April 9th 2010, 05:51 PM
  5. inverse trig values and finding inverse
    Posted in the Trigonometry Forum
    Replies: 4
    Last Post: April 6th 2009, 12:04 AM

Search Tags


/mathhelpforum @mathhelpforum