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

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Homework Help Overview

The problem involves the function f defined as f(x) = |x - 1|, and the task is to sketch the graph of y = f(f(x)). Participants are exploring how to handle the composition of the absolute value function with itself.

Discussion Character

  • Exploratory, Conceptual clarification, Mathematical reasoning

Approaches and Questions Raised

  • Participants discuss how to set up the equations for f(f(x)), questioning the validity of inserting an absolute value within another absolute value. There are attempts to clarify the process of plugging values from the original function back into itself.

Discussion Status

The discussion is ongoing, with some participants providing guidance on how to approach the problem. There is a suggestion to consider the function as a piecewise function, and participants are encouraged to plug in integer values to explore the resulting outputs.

Contextual Notes

Some participants express uncertainty about the implications of using absolute values in the composition and how to accurately represent the function graphically. There is mention of the potential for missing important details if values are simply plugged in without careful consideration.

Emworthington
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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?
 
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f(f(x))=|f(x)-1|=... Perform the last step and then start plugging in some values.
 
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?
 
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
 
Emworthington said:

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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