Question

Let f : R → R be a continuous function defined by f(x) = 1/(e^x + 2e^-x).

Statement-1: f(c) = 1/3, for some c ∈ R.

Statement-2: 0 < f(x) ≤ 1/2√2, for all x ∈ 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 

Answer 1

Answer is (D) Statement-1 is true, Statement-2 is true; Statement-2 is the correct explanation for Statement-1

Therefore, we conclude that Statement-1 is true, Statement-2 is true; Statement-2 is the correct explanation for Statement-1