# determining the domain of a fuction

• July 23rd 2012, 02:02 AM
arsenal12345
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)
• July 23rd 2012, 02:12 AM
Prove It
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 \begin{align*} x^2 - 16 &\geq 0 \\ x^2 &\geq 16 \\ |x| &\geq 4 \\ x \leq -4 \textrm{ or } x &\geq 4 \end{align*}
• July 23rd 2012, 02:19 AM
arsenal12345
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 ??
• July 23rd 2012, 02:20 AM
Prove It
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...
• July 23rd 2012, 02:27 AM
arsenal12345
Re: determining the domain of a fuction
wait i thought domain is the interval < when is the doma everything except interval ?
• July 23rd 2012, 02:30 AM
arsenal12345
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 ?
• July 23rd 2012, 06:38 AM
HallsofIvy
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 $x\le -4$ and $x\ge 4$.

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 $x^2- 16$ can be any positive number and can be 0, the range is the set of all non-negative numbers.