Results 1 to 5 of 5

Math Help - Inverse functions f-1(f(x)) where x is not in the domain

  1. #1
    Newbie
    Joined
    Jul 2011
    Posts
    3

    Question Inverse functions f-1(f(x)) where x is not in the domain

    Just a quick question because I can't quite seem to figure this out.
    They give you the equation f(x) = 1/6 [x^2 -4x +24].
    They then ask you to give the inverse function f-1(x) for which the domain is positive.
    It is then given that N is a negative real number not in the domain of f-1(x), asking you to find f-1(f(x)). I sub in the value for f(N) into f(x) then sub that back into f-1(f(x)) but it obviously just gives the number N :S.
    Just wondering how people here would approach this question.
    The answers give the answer as 4-N :S.
    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
    28

    Re: Inverse functions f-1(f(x)) where x is not in the domain

    Well first thing is to find where the domain of f is positve, while here, i'd find the range as well.

    Then find the inverse of f.

    Have a go at that.
    Follow Math Help Forum on Facebook and Google+

  3. #3
    Newbie
    Joined
    Jul 2011
    Posts
    3

    Re: Inverse functions f-1(f(x)) where x is not in the domain

    Quote Originally Posted by pickslides View Post
    Well first thing is to find where the domain of f is positve, while here, i'd find the range as well.

    Then find the inverse of f.

    Have a go at that.
    Well I managed to get the domain and range with f-1(x), x>=10/3, y>=2.
    the inverse function comes out f-1(x) = 2 + (6x - 20)^1/2.
    Both intersect at 4,4 and 6,6.
    the problem is that subbing in f(n) into f-1(n) just gives n, but the question asks for n being a negative number not in the domain, and it's answer isn't just n :S.
    Follow Math Help Forum on Facebook and Google+

  4. #4
    MHF Contributor chisigma's Avatar
    Joined
    Mar 2009
    From
    near Piacenza (Italy)
    Posts
    2,162
    Thanks
    5

    Re: Inverse functions f-1(f(x)) where x is not in the domain

    Quote Originally Posted by tomdoml View Post
    Well I managed to get the domain and range with f-1(x), x>=10/3, y>=2.
    the inverse function comes out f-1(x) = 2 + (6x - 20)^1/2.
    Both intersect at 4,4 and 6,6.
    the problem is that subbing in f(n) into f-1(n) just gives n, but the question asks for n being a negative number not in the domain, and it's answer isn't just n :S.
    The inverse function of y= \frac{x^{2}-4\ x +24}{6} is...

    x= 2 \pm \sqrt{6\ y -20} (1)

    ... so that it is a multivalued function. If x and y are vinculated to be real variables, then (1) is defined for y>\frac{10}{3}. If in general x and y are complex variables, then (1) is defined for all values of y...

    Kind regards

    \chi \sigma
    Follow Math Help Forum on Facebook and Google+

  5. #5
    MHF Contributor
    Joined
    Oct 2009
    Posts
    5,536
    Thanks
    778

    Re: Inverse functions f-1(f(x)) where x is not in the domain



    Since f(x) and f^{-1}(x) are mutually inverse, their graphs are symmetric w.r.t. the diagonal line y = x. Suppose that A has the coordinates (N,0). Calculate the coordinates of B, C, D, E and F taking into account that the red parabola is symmetric w.r.t. x = 2 and CD = DE. The y-coordinate of F is f^{-1}(f(N)).
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Replies: 4
    Last Post: April 2nd 2012, 09:17 AM
  2. inverse and the domain...
    Posted in the Algebra Forum
    Replies: 1
    Last Post: October 26th 2009, 02:18 AM
  3. domain and range of inverse trig functions
    Posted in the Trigonometry Forum
    Replies: 2
    Last Post: October 14th 2009, 03:47 AM
  4. Inverse domain
    Posted in the Trigonometry Forum
    Replies: 1
    Last Post: May 16th 2008, 09:04 AM
  5. inverse funtion domain
    Posted in the Pre-Calculus Forum
    Replies: 1
    Last Post: November 5th 2006, 01:06 PM

Search Tags


/mathhelpforum @mathhelpforum