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Let \(p(x)\) be defined on \(2 \le x \le 10\) such that

 

\(p(x) = \begin{cases} x + 1 &\quad \lfloor x \rfloor\text{ is prime} \\ p(y) + (x + 1 - \lfloor x \rfloor) &\quad \text{otherwise} \end{cases}\)

 

where \(y\) is the greatest prime factor of \(\lfloor x\rfloor.\) Express the range of \(p\) in interval notation.

 Jul 10, 2020
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The function gets bumped up by 1 at each prime, so the range of p is [2,4) U [5,7) U [8,9).

 Jul 10, 2020
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That is incorrect, thank you though.

BillyBobJoeJr  Jul 10, 2020

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