Problem with squares and roots

[BruceSpringste]

Homework Statement

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.

Homework 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).

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?

 

[Tanya Sharma]

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.

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

I am guessing it has to do with the fact that x is not defined to be ≥ 0. Any help?

No.The domain of the function is R .

 

[BruceSpringste]

Remember √x² = |x| and not simply x.

Now rewrite f(x) .

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

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

 

[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 ?

 

[BruceSpringste]

Alright now I understand completely! Thank you very much!