1. Limited time only! Sign up for a free 30min personal tutor trial with Chegg Tutors
    Dismiss Notice
Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Homework Help: Given a transformation of the plane F(x,y) = (2x+y,x-2y), find F^-1.

  1. Apr 18, 2014 #1
    1. The problem statement, all variables and given/known data
    Given a transformation of the plane F(x,y) = (2x+y,x-2y), find F-1.

    2. Relevant equations
    Actually this exercise had an item (a) which I had to prove this is a transformation. So I proved this function is injective and surjective.

    I know F(x,y) = (u,v) IFF F-1(u,v) = (x,y).


    3. The attempt at a solution
    I did it, but I don't know if this is the real solution...

    F(x,y) = (u,v) IFF F-1(u,v) = (x,y).
    u = 2x + y
    v = x - 2y
    Solving this, I concluded that: x = (v+2u)/5 and y = (u-2v)/5
    Is this the solution? F-1 = ((v+2u)/5, (u-2v)/5) or do I have to do anything else?
     
  2. jcsd
  3. Apr 18, 2014 #2

    Mark44

    Staff: Mentor

    Not quite. You should write the inverse as F-1(u, v) = ((v+2u)/5, (u-2v)/5).

    You've done most of the work already. All that's left is to show that F-1(u, v) = (x, y). Replace u and v by what you have above, and use the formula for F-1 that you found.
     
    Last edited: Apr 18, 2014
  4. Apr 18, 2014 #3

    HallsofIvy

    User Avatar
    Science Advisor

    Alternatively, your teacher may prefer functions written in "x" and "y". In that case, replace your "u" with "x" and "v" with y: [itex]F^{-1}(x, y)= ((y+ 2x)/5, (x- 2y)/5)[/itex].
     
Share this great discussion with others via Reddit, Google+, Twitter, or Facebook

Have something to add?
Draft saved Draft deleted