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Change of variables

  1. Nov 7, 2009 #1
    1. The problem statement, all variables and given/known data
    "Let f(x)=x.
    Define the change of variable y=5x.
    Then this implies g(y)=y/5.
    [we have g(y)=f(x(y))=f(y/5) and f(x)=g(y(x))=g(5x)] "

    2. Relevant equations
    N/A

    3. The attempt at a solution
    I don't understand the above statement.
    If we define y=5x, then WHY does it imply g(y)=y/5? Shouldn't it be f(y)=y/5? WHY do we need to introduce a new function g? (here we are doing a change of variable on the independent variable x, how come the dependent variable also changes?)
    Also, WHY do we have g(y)=f(x(y)) and f(x)=g(y(x))? I don't understand this.


    I think my concepts in this topic of change of variables is screwed up. Can someone please explain?
    Thank you!
     
  2. jcsd
  3. Nov 7, 2009 #2

    rock.freak667

    User Avatar
    Homework Helper

    f(x)=x

    if y=5x then x=y/5

    so that f(y/5)=y/5 right?

    since this is a function in y, we can call it g(y)

    so g(y)=f(y/5)= y/5 ⇒ g(y)=y/5
     
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