# Problem with squares and roots

1. Apr 21, 2014

### BruceSpringste

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

Hi, I am currently studying for a exam and I have noticed I have difficulty with squares and roots. I decided to take a problem from an exam so that I can illustrate the problems I am having with it.

2. Relevant equations

If f(x) = √(x+1)2 - √(x-1)2

(a) f(x) = 2; (b) f(x) = 2x; (c) f(x) = 2√x; (d) none of (a)-(c).

3. The attempt at a solution

My first instict is to remove the squares and the roots so that f(x) = x+1 - (x-1) which in turn gives me the answer (a). This is incorrect. I am guessing it has to do with the fact that x is not defined to be ≥ 0. Any help?

2. Apr 21, 2014

### Tanya Sharma

Remember √x2 = |x| and not simply x.Now rewrite f(x) .

No.The domain of the function is R .

Last edited: Apr 21, 2014
3. Apr 21, 2014

### BruceSpringste

f(x) = |x+1| - |x-1|

I'm a bit slow, where do I take it from here?

4. Apr 21, 2014

### Tanya Sharma

Good...

Now the function will be defined differently in different regions.First consider x<-1

What is the value of |x+1| when x<-1 ?
What is the value of |x-1| when x<-1 ?
What is the value of |x+1|-|x+1|when x<-1 ?

5. Apr 21, 2014

### BruceSpringste

Alright now I understand completely! Thank you very much!