SOLUTION: Hello. I need to find the natural domain of f(x)=sqrt x(16-x^2) Note: Just to be clear, "x(16-x^2)" is UNDER the square root sign. Thanks.

Question 795636: Hello.
I need to find the natural domain of f(x)=sqrt x(16-x^2)
Note: Just to be clear, "x(16-x^2)" is UNDER the square root sign.
Thanks.
Answer by josmiceli(19441) (Show Source): You can put this solution on YOUR website!

If , the function exists- it is
If or
if , also
----------------------------
If , is the square root
of a negative number, so the function
does not exist if
-----------------------
If then is
the square root of a negative times a negative,
so the function exists
-----------------------
If , f(x) does not exist because you
have the square root of a negative times a positive
which is a negative
------------------------
If , f(x) exists because you have
the square root of a positive times a positive
------------------------
Putting this together, the domain is:

----------------
Here's the plot:

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