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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.
Thanks and also please show the steps too!
