Absolute function into piecewise function

[Astraithious]

Homework Statement

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

Homework Equations

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!

 

[Samy_A]

Homework Statement

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

Homework Equations

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.

 

[member 587159]

Homework Statement

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

Homework Equations

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 Statement

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

Homework Equations

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]

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.

 

[Astraithious]

thank you everybody this was a great relief

 

[epenguin]

Knowing the answer that's what I read when I see something else!