Question

For x ∈ R, x ≠ 0 , let f₀(x) = $\frac{1}{1-x}$ and $f_{n+1}$ (x) = f₀($f_{n}$(x)), n = 0, 1, 2, .... Then the value of f₁₀₀(3) + $f_{1}\bigg (\frac{2}{3}\bigg )+f_{2}\bigg (\frac{3}{2}\bigg )$ is equal to:
(a) $\frac{8}{3}$
(b) $\frac{4}{3}$
(c) $\frac{5}{3}$
(d) $\frac{1}{3}$

Answer 1

d) $\frac{1}{3}$