Teacher is correct because if you take 0-h as h->0, the function is well defined in the neighborhood and also defined at x=0. So LHL does exist.
Our teacher said that the limit exists for this function namely, 0, but our book tells that the limit doesn't exist.
He argued that the limit exists because the domain of the function is
which includes negative nos. from -1 to zero (less than -1 will make the function imaginary).
Which is correct?