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# Piecewise-defined function problem

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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.

Jun 30, 2020

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The function gets bumped up at every prime values, so the range of p is [2,5] U [8,9].

Jun 30, 2020
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Sorry, that's incorrect. Can you expand more behind your reasoning so I can attempt your method myself?

thelizzybeth  Jun 30, 2020