The function in question, defined as f(x) = (x^2 - 1)/(x - 1), is not continuous or differentiable at x = 1 due to the undefined nature of f(1), which results in a 0/0 form. Although the (x-1) term can be canceled, this does not change the fact that the original function is undefined at that point. The discussion highlights the importance of specifying a function's domain to properly assess continuity and differentiability. The book's answer is contested, with participants agreeing that the function's definition is inadequate without clarifying its domain. Ultimately, the function cannot be considered continuous or differentiable at x = 1.