Let f:R → R be a continuous function defined by f(x) = 1/(eˣ + 2e⁻ˣ) Statement - 1: f(c) = 1/3, for some c R. Statement - 2: 0 < f(x) ≤ 1/(2 2), for all x R

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

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

(B) Statement - 1 is true, Statement - 2 is false.

(C) Statement - 1 is false, Statement - 2 is true.

Limit, Continuity and Differentiability: JEE Main 2010 Mathematics question

JEE Main 2010 · Annual, Paper 1 · Q2627

JEE Main 2010Annual, Paper 1MathematicsMediumLimit, Continuity and Differentiability420× since 2002

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