Results 1 to 4 of 4

Math Help - Composition of Two Functions

  1. #1
    Forum Admin topsquark's Avatar
    Joined
    Jan 2006
    From
    Wellsville, NY
    Posts
    9,845
    Thanks
    320
    Awards
    1

    Composition of Two Functions

    This is a question by PapaSmurf:
    2)

    Let and f(x) = 9x + k and g(x) = kx + 9.
    Find the product of all distinct k such that f(g(x)) = g(f(x)). [Word for word, no typos]
    Follow Math Help Forum on Facebook and Google+

  2. #2
    Behold, the power of SARDINES!
    TheEmptySet's Avatar
    Joined
    Feb 2008
    From
    Yuma, AZ, USA
    Posts
    3,764
    Thanks
    78
    Given that

    f(x)=9x+k \quad g(x)=kx+9

    then

    f(g(x))=9(kx+9)+k \quad \text{ and } \quad g(f(x))=k(9x+k)+9

    setting them equal and expanding gives

    9kx+81+k=9kx+k^2+9 \iff k^2-k-72=0

    Now just solve for k and multiply the two solutions together.
    Follow Math Help Forum on Facebook and Google+

  3. #3
    Newbie
    Joined
    May 2011
    Posts
    4
    Awesome, thank you

    But, I don't completely understand what you mean at the end.
    Now just solve for k and multiply the two solutions together.
    I get  k = 9, -8
    but don't understand where to go from there... would that be my answer?
    Follow Math Help Forum on Facebook and Google+

  4. #4
    Behold, the power of SARDINES!
    TheEmptySet's Avatar
    Joined
    Feb 2008
    From
    Yuma, AZ, USA
    Posts
    3,764
    Thanks
    78
    In the original problem statement is says find the product all of distinct k.

    Well you have the two distinct values of k so find their product so multiply them together.
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Composition of Functions
    Posted in the Algebra Forum
    Replies: 2
    Last Post: February 22nd 2010, 07:49 PM
  2. composition of functions
    Posted in the Pre-Calculus Forum
    Replies: 4
    Last Post: February 24th 2009, 11:46 AM
  3. composition of functions
    Posted in the Pre-Calculus Forum
    Replies: 2
    Last Post: May 12th 2008, 04:32 AM
  4. Composition of Functions
    Posted in the Pre-Calculus Forum
    Replies: 6
    Last Post: July 13th 2007, 10:50 PM
  5. composition functions
    Posted in the Pre-Calculus Forum
    Replies: 14
    Last Post: November 26th 2006, 11:49 AM

Search Tags


/mathhelpforum @mathhelpforum