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Compostion of functions

  1. Nov 19, 2012 #1
    1. The problem statement, all variables and given/known data

    Suppose f : R→R and g : R→R where g(x) = 3x + 5 and g o f(x) = x^2 - 7.
    Find the rule for f.

    2. Relevant equations



    3. The attempt at a solution

    These seem pretty simple, but I want to make sure I'm on the right track.

    3(f(x)) + 5 = x^2 - 7
    3(f(x)) = x^2 - 12
    f(x) = (x^2 - 12)/3

    How does this look?
     
    Last edited: Nov 19, 2012
  2. jcsd
  3. Nov 19, 2012 #2
    Looks correct. You could re-write f(x) as

    [tex]
    f(x) \, = \, \frac{1}{3}x^{2} \, - \, 4
    [/tex]

    but otherwise you are correct and is fine as you have written it.
     
    Last edited: Nov 19, 2012
  4. Nov 19, 2012 #3
    Okay, thanks.
     
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