For x R, x ≠ 0, Let f₀(x) = 1/(1 - x) and f n +1 (x) = f₀(f n (x)), n = 0, 1, 2,.... Then the value of f₁₀₀(3) + f₁ (2/3) + f₂ (3/2) is equal to:

Sets, Relations and Functions: JEE Main 2016 Mathematics question

JEE Main 2016 · 9 Apr, Morning shift · Q3813

JEE Main 20169 Apr, Morning shiftMathematicsHardSets, Relations and Functions168× since 2002

For x

\in

R, x

\ne

0, Let f₀(x) =

{1 \over {1 - x}}

and f_n+1 (x) = f₀(f_n(x)), n = 0, 1, 2, . . . . Then the value of f₁₀₀(3) + f₁

\left( {{2 \over 3}} \right)

+ f₂

\left( {{3 \over 2}} \right)

is equal to :