For xÎR – {0, 1}, let f 1 (x) = 1 x , f 2 (x) = 1 – x and f 3 (x) = 1 1- x be three given functions. If a function, J(x) satisfies (f2 oJof1 ) (x) = f3 (x) then J(x) is equal to:

Question:

For $x \in \mathbf{R}-\{0,1\}, \operatorname{let} f_{1}(x)=\frac{1}{x}, f_{2}(x)=1-x$ and $f_{3}(x)=\frac{1}{1-x}$ be three given functions. If a function, $\mathrm{J}(x)$ satisfies $\left(\mathrm{f}_{2} \mathrm{oJof} \mathrm{J}_{1}\right)(x)=\mathrm{f}_{3}(x)$ then $\mathrm{J}(x)$ is equal to:

  1. $f_{3}(x)$

  2. $\frac{1}{x} f_{3}(x)$

  3. $f_{2}(x)$

  4. $f_{1}(x)$


Correct Option: 1

JEE Main Previous Year 1 Question of JEE Main from Mathematics Sets, Relations and Functions chapter.
JEE Main Previous Year Jan. 09, 2019 (I)

Solution:

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