+0  
 
0
36
2
avatar

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.*

 Oct 30, 2020
 #1
avatar
0

(a) The solution is 1 <= x <= 2.

 

(b) The solution is 2 <= x <= sqrt(5).

 

(c) The solution is sqrt(5) < = x <= 3,

 

(d) There are 204 solutions.

 Oct 30, 2020
 #2
avatar
0

How did you get the answers?

 

For A), I got x is [1, 2)

 

For b), I got x has no solution.

 

For c), I got that x is [2.5, 3).

 

Mainly just confused on d) :).

 

Thank you so so much!

Guest Oct 30, 2020

15 Online Users