# Is |x^3-1| one to one?

1. Nov 24, 2012

### peripatein

1. The problem statement, all variables and given/known data

Is the function |x^3-1| one to one? Is it monotonous?

2. Relevant equations

3. The attempt at a solution

Since |x^3-1|=|y^3-1| does not necessarily imply that x=y for every x and y, I presume it is not one to one. Hence it has no inverse function.
It is also not monotonous.
Are all these statements correct?

2. Nov 24, 2012

### tiny-tim

yes

3. Nov 24, 2012

### peripatein

Hi tiny-tim,
Once again, thanks a lot! :-)

4. Nov 24, 2012

### micromass

Staff Emeritus
While the statements are correct, they are not sufficient to complete the exercise. To actually solve it, you need to find counterexamples. For example, if you want to show that $|x^3-1|$ is not one-to-one, you need to come up with two particular and distinct points x and y such that $|x^3-1|=|y^3-1|$. Just saying that it is one-to-one is not enough without counterexample.

5. Nov 24, 2012

### peripatein

Have done so, simply didn't specify it :-). Thank you, micromass!