Is that correct??
because in my calculator i have a domain =
No, it is not correct. You calculator is right (assuming you meant In order that ab> 0, a and b must have the same sign, NOT just "a> 0, b> 0". That is, either a> 0 and b> 0 or a< 0, and b< 0. x> 0 and 1- x^2> 0 gives 0< x< 1. x< 0 and 1-x^2< 1 gives x^2> 0 which is true for any x< 0. Of course, x= 0 and x= 1 are also included.
note that the three values of x that make the expression equal to 0 are x = 0 , x = 1 , and x = -1
these three values break the possible values of x into four intervals ...
, , , and
pick any value in each interval and check the value of .
if that value is positive, then that interval is in the domain.
I thought that was what I just showed you. You have, correctly, that . As I said before, if ab> 0, then either a> 0 and b> 0 or a<0 and b< 0. You must consider both possiblities.But, i solved the domain in incorrectly way.
I do not know how to solve the domain, too show x<0 in solution.