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

 

Please help me! I am really confused on how to do this problem.

 Sep 23, 2021
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(a) The set of x that works is 1 <= x < 3/2.

 

(b) The set of x that works is 2 <= x < 8/3.

 

(c) The set of x that works is 3 <= x < 11/4.

 

(d) There are 58 possible values of x.

 Sep 23, 2021

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