If f(x) = (2x+1), f(f(f(f.... f(n))))12 times = 81919. Then n = ?
2024
If f(x) = (2x+1), f(f(f(f.... f(n))))12 times = 81919. Then n = ?
- A.
12
- B.
15
- C.
19
- D.
20
Attempted by 3 students.
Show answer & explanation
Correct answer: C
Key formula: For f(x) = 2x + 1, the k-fold composition is 2^k·x + (2^k - 1).
Compute 2^12 = 4096.
Substitute into the formula: f applied 12 times gives 4096·n + (4096 - 1) = 4096·n + 4095.
Set this equal to 81919: 4096·n + 4095 = 81919. Therefore 4096·n = 81919 − 4095 = 77824.
Divide: n = 77824 / 4096 = 19.
Answer: 19.