SOLUTION: I don't understand how to do this: Find the domain of: {{{(x^2-3)sqrt(x^3-x)}}} Thanks in advance :)!

Algebra ->  Functions -> SOLUTION: I don't understand how to do this: Find the domain of: {{{(x^2-3)sqrt(x^3-x)}}} Thanks in advance :)!      Log On


   

Question 519729: I don't understand how to do this:
Find the domain of: %28x%5E2-3%29sqrt%28x%5E3-x%29
Thanks in advance :)!
Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
%28x%5E2-3%29%2Asqrt%28x%5E3-x%29
+%28x%5E2-3%29%2Asqrt%28x%2A%28x%5E2+-+1%29%29+
In the 1st factor, +x%5E2+-+3+, x can be
any real value + or -
-----------------
Of the factor inside the square root,
+x+ cannot be between 0
and 1
If that is true, the factor +x%5E2+-+1+,
will be negative, and the square root is
not a real number.
----------------
As for x between 0 and -1,
both of the factors under the square root
turn out to be negative, and (-) x (-) = +
so that is a real number.
The domain is
+x+%3E=+1+
+x+%3C=+0+
or +1+%3C=+x+%3C=+0+