Question:
Let f: (1, ∞) → (0, ∞) be a continuous function such that for every n ∈ \(\N\), f(n) is the smallest prime factor of n. Then, which of the following options is/are CORRECT ?
Let f: (1, ∞) → (0, ∞) be a continuous function such that for every n ∈ \(\N\), f(n) is the smallest prime factor of n. Then, which of the following options is/are CORRECT ?
Updated On: Aug 13, 2024
- \(\lim\limits_{x\rightarrow \infin}f(x)\) exists
- \(\lim\limits_{x\rightarrow \infin}f(x)\) does not exists
- The set of solutions to the equation f(x) = 2024 is finite
- The set of solutions to the equation f(x) = 2024 is infinite
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The Correct Option is B, D
Solution and Explanation
The correct option is (B) : \(\lim\limits_{x\rightarrow \infin}f(x)\) does not exists and (D) : The set of solutions to the equation f(x) = 2024 is infinite.
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