find domain and range of function f= {(x, 1/1-x 2 ):x belongs to R?

Now, Let y = f(x) 

then

 

Hence, range of f(x) is all real nos. : y <0 and y≥1

 

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 f(x)= 1/1-x2,

Denominator should not be equal to 0 as 1/0 is not defined. 1-x2 not= 0. X not= +-1.

Since x2 is always +, putting x=0 will give f(x)=1, else any other no. will give ans. < 1.

So, domain= R - {1,-1}     Range= (-infinity,2) - {0}

ex: 1/1-0.5^2  = 1/0.75 =4/3 So, it will lie up to 2, but f(x) cant be zero !

Plz confirm this ans and also tell me if it is right...

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