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Homework Help: F(f(x)) when f(x) = absolute value of x-1

  1. Jan 31, 2012 #1
    1. The problem statement, all variables and given/known data
    Suppose f is the function defined by f(x) = l x-1 l Sketch the graph of y = f(f(x))

    2. Relevant equations

    3. The attempt at a solution
    It's not so much sketching the graph that is the problem as much as it is figuring out how to set up the equations. How do I put an absolute value into an equation that already has one? I sketched a table so that I had x and y values of the original function, can that help me at all?
  2. jcsd
  3. Jan 31, 2012 #2
    f(f(x))=|f(x)-1|=... Perform the last step and then start plugging in some values.
  4. Jan 31, 2012 #3
    so can I put an absolute value inside another absolute value? The function would look something like this?
    I x-1I -1 I

    Would it be valid to take the y values from the original function and plug them back into the original function?
  5. Jan 31, 2012 #4
    Yes, It would look like that. What it means is take the absolute value of x-1, and then subtract 1 from that quantity and take the absolute value of what you get from that.

    Just plug in integers for x and see what y ends up being to get the graph
  6. Jan 31, 2012 #5


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    Hello Emworthington. Welcome to PF !

    f(f(x)) = | |x-1| -1 | .

    My suggestion is to write this as a piecewise function.

    If you simply plug-in some values, you're likely to miss some important details that should be in the graph.
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