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JEE Math Practice Question

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 :

  1. A.$${8 \over 3}$$
  2. B.$${5 \over 3}$$
  3. C.$${4 \over 3}$$
  4. D.$${1 \over 3}$$

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