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Function Composition

  1. Sep 18, 2005 #1
    Hello, I've been an intermittent poster here for about five years. I've come back for another shot at PF. So for a first thread:

    Class is a currently a review of old topics. One of them is 'function composition.' I was doing an assignment today and came upon a question that required one to graph f(g(x)) from two graphs given f(x) and g(x). There were no equations supplied. How might one go about graphing f(g(x))? I am not sure of the relationship here, unfortunately.
     
  2. jcsd
  3. Sep 18, 2005 #2
    It sounds like you have two graphs, and have to generate a third one, f(g(x)) from the graphs of f(x) and g(x)?

    Well, right now, you have y=g(x) and y=f(x). But you want a graph which is y=f(g(x)). Is this enough to get you started? This sounds like a pain, BTW.

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  4. Sep 18, 2005 #3
    Yes, this is correct. I have two graphs - f(x) and g(x) - and I need to generate the third, f(g(x)).

    I know that y=g(x) and y=f(x), but I'm not sure how to generate y=f(g(x)) from that.
     
  5. Sep 18, 2005 #4
    let x=g(x), to sub into the equation y = f(x)? dunno if its an help. its a strange question.
     
    Last edited: Sep 18, 2005
  6. Sep 18, 2005 #5
    The only difference is that you have to look up the values on the graphs, instead of compute them. A = g(x), y = f(A), this is how you would compute a function composition, right? These X's and Y's would be the coord's of the point on the new graph. The intermediate value of A is just used to look up the proper value of the function composition.

    I'm assuming here that the graphs are complicated, and it's not possible to recover the functions that generated them. If they are simple, like a straight line or a parabola, then you could recover the functions (or make a good guess) and generate a formula to plot the new graph directly.

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