Let $$f : [1,3] \to R$$ be a function satisfying $$\frac{x}{[x]} \le f(x) \le \sqrt{6-x}$$, for all $$x \neq 2$$ and $$f(2) = 1$$, where $$R$$ is the set of all real numbers and $$[x]$$ denotes the largest integer less than or equal to $$x$$. Statement 1: $$\lim_{x\to 2} f(x)$$ exists. Statement 2: $$f$$ is continuous at $$x = 2$$.

A

Statement 1 is true, Statement 2 is true, Statement 2 is a correct explanation for Statement 1.

B

Statement 1 is false, Statement 2 is true.

C

Statement 1 is true, Statement 2 is true, Statement 2 is not a correct explanation for Statement 1.

D

Statement 1 is true, Statement 2 is false.