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# Floor Function Question

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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 \(0 \le x \le 10\)

Hint: Divide into cases, based on the value of \(\lfloor x \rfloor. \)

-------------Thanks!

(Note that (a), (b) and (c) are subquestions that lead up to the "total question," (d).)

Jun 12, 2020