JEE Mains · Maths · STD 12 - 1. relation and function
For \(x \in R -\{0,1\},\) \({f_1}\left( x \right) = \frac{1}{x},{f_2}\left( x \right) = 1 - x\) and \(f_{3}(x)=\frac{1}{1-x}\) be three given functions. If a function, \(J ( x )\) satisfies \(\left( {{f_2}oJo{f_1}} \right)\left( x \right)= f _{3}( x )\) then \(J ( x )\) is equal to
- A \({f_3}\,\left( x \right)\)
- B \(\frac{1}{x}\,{f_3}\,\left( x \right)\)
- C \({f_2}\,\left( x \right)\)
- D \({f_1}\,\left( x \right)\)
Answer & Solution
Correct Answer
(A) \({f_3}\,\left( x \right)\)
Step-by-step Solution
Detailed explanation
\(x \in R - \left( {0,1} \right)\) \({f_1}\left( x \right) = \frac{1}{x},{f_2}\left( x \right) = 1 - x,{f_3}\left( x \right) = \frac{1}{{1 - x}}\) Given \({f_2}\left( {J\left( {{f_1}\left( x \right)} \right)} \right) = {f_3}\left( x \right)\)…
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