Let $$f: R \to R$$ be a continuous function defined by $$f(x) = \frac{1}{e^x + 2 e^{-x}}$$. Statement-1: $$f(c) = \frac{1}{3}$$, for some $$c \in R$$. Statement-2: $$0 < f(x) \le \frac{1}{2\sqrt{2}}$$, for all $$x \in R$$.

A

Statement-1 is true, Statement-2 is true; Statement-2 is not the correct explanation for Statement-1

B

Statement-1 is true, Statement-2 is false

C

Statement-1 is false, Statement-2 is true

D

Statement-1 is true, Statement-2 is true; Statement-2 is the correct explanation for Statement-1