determining the domain of a fuction

So Determine the domain of this fuction

y=√x^2-16

so first i factorised and get (x+4) and (x-4)

i m sure the domain has to be between -4 <x<4

what i am confused about is what happens to the square root , can some 1 how me how to do the proper workout for this problem ?

cheers (Rofl)

Re: determining the domain of a fuction

Quote:

Originally Posted by

**arsenal12345** So Determine the domain of this fuction

y=√x^2-16

so first i factorised and get (x+4) and (x-4)

i m sure the domain has to be between -4 <x<4

what i am confused about is what happens to the square root , can some 1 how me how to do the proper workout for this problem ?

cheers (Rofl)

Nothing negative can go inside a square root. So

$\displaystyle \displaystyle \begin{align*} x^2 - 16 &\geq 0 \\ x^2 &\geq 16 \\ |x| &\geq 4 \\ x \leq -4 \textrm{ or } x &\geq 4 \end{align*}$

Re: determining the domain of a fuction

thanks buddy :) would it be wrong if i wrote down domain is present in the fuction between -4 <x<4 ??

Re: determining the domain of a fuction

Quote:

Originally Posted by

**arsenal12345** thanks buddy :) would it be wrong if i wrote down domain is present in the fuction between -4 <x<4 ??

Of course it would be wrong. The domain is everything EXCEPT for that interval...

Re: determining the domain of a fuction

wait i thought domain is the interval < when is the doma everything except interval ?

Re: determining the domain of a fuction

is it like when the y is real the domain is the interrval and when its not the domain is every thing except the interval ??

if yes how do i workout y ?

Re: determining the domain of a fuction

You were told that in Prove It's first response to your post: the quantity inside the square root must be non-negative and that happens for $\displaystyle x\le -4$ and $\displaystyle x\ge 4$.

I don't know what you mean by "work out y". If you mean just calculate y, for a given x, do exactly what the formula says: square x, subtract 16, then take the square root. If you mean that you want to find the **range** of the function, the set of all possible values of y, then you can note that a square root is never negative but, since $\displaystyle x^2- 16$ can be any positive number and can be 0, the range is the set of all non-negative numbers.