# Thread: Domain And Range Question

1. ## Domain And Range Question

Hello Everyone, I have a small question, any help woulkd be appreciated
This is my first time using latex so excuse my errors if any are made

$\displaystyle f(x)=\frac{1}{\sqrt x^2-16}$

The question is too find the domain and range

EDIT: The Square root is meant to go on the x^2 and the -16 ($\displaystyle \sqrt {x^2-16}$) Like This

2. ## Re: Domain And Range Question

So your function is $\displaystyle \displaystyle f(x) = \frac{1}{\sqrt{x^2 - 16}}$. Do you see any natural restrictions from a variable denominator or a square root function?

3. ## Re: Domain And Range Question

Im Not sure what you mean by natural restriction, if you mean the (x+4)(x-4) section

4. ## Re: Domain And Range Question

Surely you know some things like you can't have zero denominators or that you can only take square roots of nonnegative numbers?

5. ## Re: Domain And Range Question

Originally Posted by Prove It
Surely you know some things like you can't have zero denominators or that you can only take square roots of nonnegative numbers?
Yes Of course and after a bit of work I came to this concusion x<-4 & x>4 ( as anynumbers tghat are less than 16 or 0 will make the function invalid as there cannot be a negative number or a 0 in the Denominator with a square root

Would this be Correct

domain: x<-4 & x>4
Range y>0

Correct