JEE Math Practice Question

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

1. A.Statement - 1 is true, Statement -2 is true; Statement - 2 is not a correct explanation for Statement - 1.
2. B.Statement - 1 is true, Statement - 2 is false.
3. C.Statement - 1 is false, Statement - 2 is true.
4. D.Statement - 1 is true, Statement -2 is true; Statement -2 is a correct explanation for Statement - 1.