Let f: R → R be a function defined by f(x) = (2e²ˣ)/(e²ˣ + e). Then f(1/100) + f(2/100) + f(3/100) +..... + f(99/100) is equal to _ _ _ _ _ _ _.

Sets, Relations and Functions: JEE Main 2022 Mathematics question

JEE Main 2022 · 27 Jun, Morning shift · Q32

JEE Main 202227 Jun, Morning shiftMathematicsMediumSets, Relations and Functions168× since 2002

Let f : R

\to

R be a function defined by

f(x) = {{2{e^{2x}}} \over {{e^{2x}} + e}}

. Then

f\left( {{1 \over {100}}} \right) + f\left( {{2 \over {100}}} \right) + f\left( {{3 \over {100}}} \right) + \,\,\,.....\,\,\, + \,\,\,f\left( {{{99} \over {100}}} \right)

is equal to ______________.

Your answerType your answer. Integers and decimals are accepted.