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How many different values can \(\lfloor x \rfloor + \lfloor 2x \rfloor + \lfloor 3x \rfloor +\lfloor 4x \rfloor\) take for x?

 Aug 4, 2023
 #2
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PLS HELP ASAP:

 

1. What is the range of the function \(G(x) = |x+1|-|x-1|~\)Express your answer in interval notation.

 Aug 4, 2023
 #3
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The function floor(x) + floor(2x) + floor(3x) + floor(4x) takes on different values for 0 <= x <= 1 if and only if the fractional part {x} of x satisfies 0 <= {x} < 1/4. The different values that {x} can take on in this range are 0, 1/4, 2/4, 3/4, and 1. Therefore, the function floor(x) + floor(2x) + floor(3x) + floor(4x) takes on 1 + 4 = 5 different values in the range 0 <= x <= 1.

 Aug 4, 2023

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