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Homework Help: I need help with 1 question. VERY PLEASE!

  1. Oct 16, 2007 #1
    I need help with 1 question. VERY URGENT PLEASE!

    1. The problem statement, all variables and given/known data
    if F[g(x)] = R(x) where g(x) and r(x) is known find f(x).


    2. Relevant equations
    none


    3. The attempt at a solution
    I did it but i dont know if it is right:

    (g^-1 of x) = x

    so...

    F(x) = r(g^-1 of x)
     
  2. jcsd
  3. Oct 16, 2007 #2
    f(x)=R(x)/g(x)
     
  4. Oct 16, 2007 #3

    how did u get that?
     
  5. Oct 16, 2007 #4
    Well I'm not 100% certain its that but I just used logic. Division is the inverse of multiplication so if f[g(x)]=R(x) then f(x)=R(x)/g(x). i.e. f[g(2)]=12 then f(x)=12/2. 12/2=6 and 6(2)=12
     
  6. Oct 16, 2007 #5

    Dick

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    It's not multiplication. It's composition of functions. And assuming g is invertible then the OP is correct. Except don't say g^(-1)(x)=x. That's ridiculous. g(g^(-1)(x))=x.
     
    Last edited: Oct 16, 2007
  7. Oct 17, 2007 #6

    EnumaElish

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    Isn't the OP correct only if F(g) = g(F) and R(g) = g(R) ?
     
  8. Oct 17, 2007 #7

    Dick

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    No. The OP is ok with the answer. What the OP means to say is substitute y=g(x), so x=g^(-1)(y). So F(y)=R(g^(-1)(y)). Now just replace the dummy y with x.
     
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