Q 1124580451.     Let `f: R` to `R` be a continuous function defined by `f(x) = 1/(e^x + 2e^-x).`

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

Statement-2: ` 0` < `f(x) <= 1/(2 sqrt(2)),` for all `x` in `R`

JEE 2010 Mains
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

HINT

Since `e^x + 2e^-x` is always positive, `f(x) > 0` `f(x) = e^x/(e^(2x) + 2)`

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