+133 Let \(f(x) = \lfloor x \lfloor x \rfloor \rfloor\) for \(x \ge 0.\)
(a) Find all \(x \ge 0\) such that \(f(x) = 1.\)
(b) Find all \(x \ge 0\) such that \(f(x) = 3.\)
(c) Find all \(x \ge 0\) such that \(f(x) = 5.\)
(d) Find the number of possible values of \(f(x)\) for \(0 \le x \le 10.\)
