For x $ \in $ R, x $ \ne $ 0, Let f0(x) = ${1 \over {1 - x}}$ and fn+1 (x) = f0(fn(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 :

Question

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 :

${8 \over 3}$