The implicit domain is \( (-\infty,1)\cup(1,\infty)\). To find the range, replace \(f(x)\) with \(y\) and solve for \(x\) to get \(x=\dfrac{y-1}{y-2}\). So \(y\) cannot equal to 2. Thus the range of the function is \((-\infty,2)\cup(2,\infty)\).