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A recursive function h, is defined as follows :
h(m) = k, if m = 0
= 1, if m = 1
= 2 h(m – 1) + 4h(m – 2), if m ≥ 2
If the value of h(4) is 88 then the value of k is :
  • a)
    0
  • b)
    1
  • c)
    2
  • d)
    -1
Correct answer is option 'C'. Can you explain this answer?
Most Upvoted Answer
A recursive function h, is defined as follows :h(m) = k, if m = 0= 1, ...
According to given question:
h(4) = 88
88 = 2 h(3) + 4 h(2)
= 2 [2 h(2) + 4 h(1)] + 4 h(2)
= 8 h(2) + 8 h(1)
= 8 (2 + 4 k) + 8
= 24 + 32 k
 i.e.   k = 2
So, option (C) is corrct.
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Community Answer
A recursive function h, is defined as follows :h(m) = k, if m = 0= 1, ...
- 1), if m > 1 and m is odd= h(m/2), if m > 1 and m is even

This function can be used to generate a sequence of numbers starting from any given number m, by applying the function repeatedly to generate the next number in the sequence. For example, starting from m = 6, the sequence generated by the function would be:

h(6) = h(3) = h(2) = h(1) = 1
h(4) = h(2) = h(1) = 1
h(5) = h(4) = h(2) = h(1) = 1

So the sequence starting from 6 would be: 6, 3, 2, 1, 1, 1, ...

This function is sometimes used in computer science for various algorithms, including the analysis of certain sorting algorithms. It is also related to the Collatz conjecture, which is a famous unsolved problem in mathematics.
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