For x R,x 0 Î ¹ , let f0 (x) = 1 1 x – and fn+1 (x) = f0 (fn (x)), n = 0, 1, 2, …. Then the value of f100(3) + 1 2 2 3 f f 3 2 æö æö ç÷ ç÷ + èø èø is equal to :

Question:

For $x \in R, x \neq 0$, let $f_{0}(x)=\frac{1}{1-x}$ and $f_{n+1}(x)=f_{0}\left(f_{n}(x)\right)$, $\mathrm{n}=0,1,2, \ldots .$ Then the value of $\mathrm{f}_{100}(3)+\mathrm{f}_{1}\left(\frac{2}{3}\right)+\mathrm{f}_{2}\left(\frac{3}{2}\right)$ is equal to:

  1. $\frac{8}{3}$

  2. $\frac{4}{3}$

  3. $\frac{5}{3}$

  4. $\frac{1}{3}$


Correct Option: 3

JEE Main Previous Year 1 Question of JEE Main from Mathematics Sets, Relations and Functions chapter.
JEE Main Previous Year Online April 9, 2016

Solution:

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