# Absolute function into piecewise function

## Homework Statement

Write F(x)= x2-5|x| as a piecewise function

## The Attempt at a Solution

I was writting it out and came to
Fx= x2-5(x) and x2-5(-x)

but my book says that it comes out to be
x2-5
x2-5(-x)

I imagine there is a very simple reason why the x in the first one disappears but i would love an explanation, thank you!

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Samy_A
Homework Helper

## Homework Statement

Write F(x)= x2-5|x| as a piecewise function

## The Attempt at a Solution

I was writting it out and came to
Fx= x2-5(x) and x2-5(-x)

but my book says that it comes out to be
x2-5
x2-5(-x)

I imagine there is a very simple reason why the x in the first one disappears but i would love an explanation, thank you!
Looks like a typo in the book.

For positive x, you indeed get F(x)=x²-5x, and for negative x you get F(x)=x²+5x.

Math_QED
Homework Helper
2019 Award

## Homework Statement

Write F(x)= x2-5|x| as a piecewise function

## The Attempt at a Solution

I was writting it out and came to
Fx= x2-5(x) and x2-5(-x)

but my book says that it comes out to be
x2-5
x2-5(-x)

I imagine there is a very simple reason why the x in the first one disappears but i would love an explanation, thank you!
You can verify that the book is wrong by filling in x values

epenguin
Homework Helper
Gold Member

## Homework Statement

Write F(x)= x2-5|x| as a piecewise function

## The Attempt at a Solution

I was writting it out and came to
Fx= x2-5(x) and x2-5(-x)

but my book says that it comes out to be
x2-5
x2-5(-x)

I imagine there is a very simple reason why the x in the first one disappears but i would love an explanation, thank you!
Your answers appear to be identical with the book's so I don't know what your problem is. It would then be usual to write it in the form that Samy did, and also when setting out piecewise functions you have to indicate the range either side of the form.

haruspex
Homework Helper
Gold Member
Your answers appear to be identical with the book's so I don't know what your problem is.
No, the book has x2-5 instead of x2-5x.

thank you everybody this was a great relief

epenguin
Homework Helper
Gold Member
Knowing the answer that's what I read when I see something else!