Results 1 to 6 of 6

Math Help - Inverse

  1. #1
    Super Member
    Joined
    Oct 2006
    Posts
    679
    Awards
    1

    Inverse

    Inverse Function:
    Attached Thumbnails Attached Thumbnails Inverse-50.gif  
    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 qbkr21 View Post
    Inverse Function:
    there is a formula that says: \left(f^{-1} \right)'(a) = \frac {1}{f' \left( f^{-1}(a) \right)} ...i can show you how to derive this if you are interested.

    can you continue? the only problem here really, is finding f^{-1}(a), do you think you can do that?
    Follow Math Help Forum on Facebook and Google+

  3. #3
    Super Member
    Joined
    Oct 2006
    Posts
    679
    Awards
    1

    Re:

    Quote Originally Posted by Jhevon View Post
    there is a formula that says: \left(f^{-1} \right)'(a) = \frac {1}{f' \left( f^{-1}(a) \right)}

    can you continue? the only problem here really, is finding f^{-1}(a), do you think you can do that?

    No, this is seemingly where I get stuck. If you wouldn't mind could you please just work this one out, so that I can print it off and use it as an example for other problems. Thanks so much!

    -qbkr21
    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 qbkr21 View Post
    No, this is seemingly where I get stuck. If you wouldn't mind could you please just work this one out, so that I can print it off and use it as an example for other problems. Thanks so much!

    -qbkr21
    So we know \left(f^{-1} \right)'(a) = \frac {1}{f' \left( f^{-1}(a) \right)}

    and we wish to find \left(f^{-1} \right)'(1) for the function f(x) = x^3 + x + 1

    You know that f'(x) = 3x^2 + 1

    Now we need to find f^{-1}(1)

    Recall that the inverse function is a function that takes an output value back to its preimage (or input value). So saying we want to find f^{-1}(1) is saying that we want to find an x such that f(x) = 1

    Now I don't really know any shortcuts here, it's just something you have to figure out by working backwards in your head. usually they give you functions where it is easy to tell what x gives you the desired value. Here it is obviously 0, since f(0) = 0^3 + 0 + 1 = 1. Therefore f^{-1}(1) = 0 since f(0) = 1

    So now, finally, we plug it into our formula:

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

    .............. = \frac {1}{f' \left(0 \right)}

    .............. = \frac {1}{3(0)^2 + 1}

    .............. = 1
    Follow Math Help Forum on Facebook and Google+

  5. #5
    Super Member
    Joined
    Oct 2006
    Posts
    679
    Awards
    1

    Re:

    Jhevon you are the freaking MAN!! A true Jedi Master!!

    OK so let me get this straight...

    1) Take the derivative of the function
    2) Set the function = to that "a" value and solve for X
    3) 1/derivative and place the "X" value from step 2 where x is in the (f^-1)'(a) formula?

    Is this correct?

    Thanks Buddy!

    -qbkr21
    Follow Math Help Forum on Facebook and Google+

  6. #6
    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 qbkr21 View Post
    Jhevon you are the freaking MAN!! A true Jedi Master!!

    OK so let me get this straight...

    1) Take the derivative of the function
    2) Set the function = to that "a" value and solve for X
    3) 1/derivative and place the "X" value from step 2 where x is in the (f^-1)'(a) formula?

    Is this correct?

    Thanks Buddy!

    -qbkr21
    correct, but it is "1/derivative and place the "X" value from step 2 where a is in the (f^-1)'(a) formula?"...but i think that's what you meant
    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, 04:58 PM
  2. Inverse tan and inverse of tanh
    Posted in the Calculus Forum
    Replies: 2
    Last Post: October 31st 2010, 07:20 AM
  3. secant inverse in terms of cosine inverse?
    Posted in the Trigonometry Forum
    Replies: 1
    Last Post: August 30th 2010, 09:08 PM
  4. Replies: 1
    Last Post: April 9th 2010, 06:51 PM
  5. inverse trig values and finding inverse
    Posted in the Trigonometry Forum
    Replies: 4
    Last Post: April 6th 2009, 01:04 AM

Search Tags


/mathhelpforum @mathhelpforum