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F(g(x)) chain rule help

  1. May 4, 2008 #1
    ok so f(g(x)) = x, for all x.

    f(3)=8
    f'(3)=9

    what are the values of g(8) and g'(8)

    ok, so g(8) = 3

    because f(g(8)) must equal 8, and f(3) = 8, so g(x) must equal three.

    however, i have NO idea how to do g'(x)

    i was thinking of using the chain rule, but this gets me nowhere..help!!

    f'(g(x))*g'(x) = 8 ?? is this correct?? then wouldnt g'(x) = 1 ??
     
    Last edited: May 4, 2008
  2. jcsd
  3. May 4, 2008 #2

    Vid

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    chain rule
     
  4. May 4, 2008 #3

    HallsofIvy

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    What fiziksfun wrote in his last line is the chain rule, not the product rule.
    If (f(g(x))= x then f'(g(x))*g'(x)= (x)'= 1, not 8.
     
  5. May 4, 2008 #4
    the chain rule doesn't get me anywhere :[
     
  6. May 4, 2008 #5
    how do you know (x)' is equal to 1 ???
     
  7. May 4, 2008 #6

    Vid

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    Yea, I saw product rule in his post and just skipped over the symbols.
     
  8. May 4, 2008 #7
    oh wait, is it because d/dx(x) = 1 ?? YAY!!
     
  9. May 4, 2008 #8

    HallsofIvy

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    Wow, that was fast!

    I must admit that when you asked how I knew that the derivative of x was 1, I started to reach for my 2 by 4!
     
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