CMI2016-B-7aii

Question

Consider the funciton $M$ defined as follows:

$M(n) = \begin{cases} n-10 & \text{ if } n > 100 \\ M(M(n+11)) & \text{ if } n \leq 100 \end{cases}$

Compute the following$: M(99)$

Answer 1

M(99) $= M(M(99 + 11))\\ = M(M(110))\\ =M(100)\\ = M(M(111))\\ = M(101)\\ = 91$

Answer 2

solving without using any Algorithim.

$M\left ( 100 \right )$=$M\left ( M\left ( 99 + 11 \right ) \right )$

                              =$M\left ( 101 \right )$

                                           $\because M\left ( 111 \right )=111-10=101$  
                               

                               =$91$

Now, $M \left ( 99 \right )$ = $M \left ( \left M ( 99+11 \right ) \right )$

                                  =$M\left ( M\left ( 110 \right )\right ) $

                                  =$M\left ( 100 \right )=91$