Let f: (1, ∞) → (0, ∞) be a continuous function such that fo... | Real Analysis | SolveeIt | Solveeit

Today, August 23

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 ?

A

$\lim\limits_{x\rightarrow \infin}f(x)$ exists

B

$\lim\limits_{x\rightarrow \infin}f(x)$ does not exists

C

The set of solutions to the equation f(x) = 2024 is finite

D

The set of solutions to the equation f(x) = 2024 is infinite

Answer

$\lim\limits_{x\rightarrow \infin}f(x)$ does not exists

Explanation

Solution

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.