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JEE Main 201815 AprilEvening ShiftOnline
Exam
JEE Main
Year
2018
Date
15 April
Shift
Evening Shift
Mode
Online
Subject
Mathematics
Chapter
Functions

JEE Main 2018 · 15 April · Evening Shift · Online · Mathematics · Functions

Let f: A arrow B be a function defined as f(x)= (x-1)/(x-2) , where...

Let f:A→f: \mathrm{A} \rightarrow B be a function defined as f(x)=f(x)= x−1x−2\frac{x-1}{x-2}, where A=R−{2}A=R-\{2\} and B=R−{1}B=R-\{1\}. Then ff is

Options

  1. Ainvertible and f−1(y)=2y+1y−1f^{-1}(y)=\frac{2 y+1}{y-1}
  2. Binvertible and f−1(y)=3y−1y−1f^{-1}(y)=\frac{3 y-1}{y-1}
  3. Cno invertible
  4. Dinvertible and f−1(y)=2y−1y−1f^{-1}(y)=\frac{2 y-1}{y-1}

Correct answer

D. invertible and f−1(y)=2y−1y−1f^{-1}(y)=\frac{2 y-1}{y-1}

Step-by-step solution

Suppose y=f(x)y=f(x)⇒y=x−1x−2⇒yx−2y=x−1⇒(y−1)x=2y−1⇒x=f−1(y)=2y−1y−1\begin{aligned}&\Rightarrow y=\frac{x-1}{x-2}\\ &\Rightarrow y x-2 y=x-1 \\ &\Rightarrow(y-1) x=2 y-1 \\ &\Rightarrow x=f^{-1}(y)=\frac{2 y-1}{y-1} \end{aligned}$$As the function is invertible on the given domain and its inverse can be obtained as above.
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