domain and range

Note  that the function  is NOT defined at x  = 0

When x  is  a large negative, f(x)  =  is only slightly  negative, but not  0

When  x is a very small negative,  f(x) is an extremely LARGE negative  verging towards  - inf

When  x is a small positive, f(x)  is a LARGE positive verging towards + inf

When x  is  a large positive, f(x) is only slightly positive, but  not  0

So....the  range  is   (-inf , 0)  U (0 , + inf)

The graph here confirms this  :  https://www.desmos.com/calculator/fmxqof7zjz