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 \(0 \le x \le 10.\)

Thank you in advance! Help is appreciated greatly :).

*I mostly understand a)-c), but d) is just confusing I guess.*

Guest Oct 30, 2020