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Fg(x) - terminology

  1. May 29, 2008 #1
    It's just the terminology but im just unsure what it means
    I have 2 functions
    f(x) = ln(2x-1)
    g(x) = [tex]\frac{2}{x-3}[/tex]

    the question is find the exact value of fg(4)

    now what exaclty does that mean. I'm guessing we sub x = 4 into it at some point. It is asking for me to mulitply f(x) by g(x)

    im not sure. can someone help me please. thanks
  2. jcsd
  3. May 29, 2008 #2


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    I'm also not sure. Normally "fg(x)" means "f(x)*g(x)". That is, to find fg(4) you substitute x= 4 into both equations, then multiply the values. That is probably what is meant.

    But it is possible that what you really mean is [itex]f \circle g(x)[/itex] which means f(g(x)). That is, substitute x= 4 into g: g(4). Then, whatever number you get for g(4), substitute that into f: f(g(4)).

    Surely your textbook was discussing one or the other of those?
  4. May 29, 2008 #3
  5. May 29, 2008 #4


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    Okay, it does mean "composition of functions": f(g(x)). First find g(4)= 2/(4-3)= 2/1= 2 and then find f(2). Strictly speaking, that should be written with a little "o" between the functions.
  6. May 29, 2008 #5
    ahh cheerz i understand now, but can you explain part b. I though ^-1 means 1 over the term

    ie x^(-1) = 1/x

    What is part b asking really

    thanks :)
  7. May 29, 2008 #6
    No. f^(-1)(x) means the inverse function of f(x).
    So if y=f(x)=ln(2x-1), then you should solve for x and replace x by y and y by x. Then you have the inverse of f(x).
  8. May 29, 2008 #7


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    For a number, x, x-1 means 1/x. For a function, f, f-1 means the inverse function, f(f-1(x))= x, f-1(f(x))= x. It's an unfortunate conflict of symbols but too late to change it now!
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