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

  • #1

Homework Statement


Suppose f is the function defined by f(x) = l x-1 l Sketch the graph of y = f(f(x))


Homework Equations





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?
 

Answers and Replies

  • #2
294
1
f(f(x))=|f(x)-1|=... Perform the last step and then start plugging in some values.
 
  • #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?
 
  • #4
19
0
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
 
  • #5
SammyS
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Homework Statement


Suppose f is the function defined by f(x) = l x-1 l Sketch the graph of y = f(f(x))

Homework Equations



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?
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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