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GATE CS 2022 Set 1 — Question 51

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MSQ+2 / -0HardRecurrence RelationsSets & CombinatoricsEngineering Mathematics

Engineering Mathematics → Sets & Combinatorics → Recurrence Relations

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Question

Consider the following recurrence:f(1)=1;f(2n)=2f(n)−1,for n≥1;f(2n+1)=2f(n)+1,for n≥1.\begin{aligned} f(1) &= 1; \\ f(2n) &= 2f(n) - 1, & \text{for } n \ge 1; \\ f(2n + 1) &= 2f(n) + 1, & \text{for } n \ge 1. \end{aligned}Then, which of the following statements is/are TRUE?
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