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 $x \in R$

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 $x \in R$

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

Statement - 1 is true, Statement - 2 is false.

Statement - 1 is false, Statement - 2 is true.

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

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