SOLUTION: find the domain and range of f(x) = (x)/(sqrt(1 - ((sqrt(- x)))^2))

   

find the domain and range of 



x cannot be positive but can be 0. The denominator is always positive.
So the value of f is never positive but can be 0 when x=0.

What is under the radical in the denominator must be positive, not negative or
0.  Remember that -x can never be negative.







Remember again that -x is non-negative. 



 and since x is never positive but can be 0,

the domain is 

We set the denominator = 0 to find the vertical asymptote:









Remember that -x is non-negative. 





So the vertical asymptote is , indicated by the green line.

The domain is 

The range is 

Edwin

Notice that I have added something to the above answer.  This part:

What is under the radical in the denominator must be positive, not negative or
0.  Remember that -x can never be negative.







Remember again that -x is non-negative. 



 and since x is never positive but can be 0,

the domain is 

Edwin