Results 1 to 2 of 2

Math Help - Finding the inverse of a function

  1. #1
    Junior Member
    Joined
    Apr 2009
    Posts
    38

    Finding the inverse of a function

    I need help finding the inverse for this function

    g:[-1,\infty) \rightarrow, g(x) = x^2+2x

    What I've done so far.

    Let g(x) = y

    y=x^2+2x

    Swap x and y, and solve for y

    x=y^2+2y

    x=y(y+2)

    I'm stuck here, can anyone please help?

    Nevermind, I got it, had to complete the square!
    Follow Math Help Forum on Facebook and Google+

  2. #2
    Member rowe's Avatar
    Joined
    Jul 2009
    Posts
    89
    I had typed this up by the time I saw your last comment, d'oh- so I post anyways.

    g(x) = x^2+2x

    Set g(x) to y:

    y = x^2+2x

    Complete that square:

    y = (x+1)^2 - 1

    y + 1 = (x+1)^2

    \sqrt{y+1} - 1 = x

    Swap x and y, so that y=g^{-1}(x) = \sqrt{y+1}-1

    Prove to check; it should be that f(g(x)) = g(f(x)) = x, here's an example:

    g(f(x)) = \sqrt{x^2+2x+1} - 1

    g(f(x)) = \sqrt{(x+1)^2} - 1

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

    g(f(x)) = x
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Finding a Function's Inverse
    Posted in the Algebra Forum
    Replies: 1
    Last Post: April 6th 2010, 02:48 PM
  2. Finding inverse of this function?
    Posted in the Pre-Calculus Forum
    Replies: 1
    Last Post: February 2nd 2010, 10:53 PM
  3. Finding inverse function
    Posted in the Pre-Calculus Forum
    Replies: 4
    Last Post: December 7th 2009, 06:50 PM
  4. finding the inverse of a function
    Posted in the Calculus Forum
    Replies: 8
    Last Post: October 15th 2009, 09:54 PM
  5. Finding the inverse of a function
    Posted in the Algebra Forum
    Replies: 1
    Last Post: September 11th 2009, 06:28 PM

Search Tags


/mathhelpforum @mathhelpforum