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

## Homework Statement

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

## 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?

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

SammyS
Staff Emeritus
Homework Helper
Gold Member

## Homework Statement

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

## 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.