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JEE Main201815 Apr 2018Evening ShiftMathematicsFunctionsActual

Let f: A B be a function defined as f(x)= x-1 x-2 , where A=R- 2 and B=R- 1 . Then f is

Options

  1. Ainvertible and f⁻¹(y)= 2 y+1 y-1
  2. Binvertible and f⁻¹(y)= 3 y-1 y-1
  3. Cno invertible
  4. Dinvertible and f⁻¹(y)= 2 y-1 y-1

Correct answer

D. invertible and f⁻¹(y)= 2 y-1 y-1

Step-by-step solution

Suppose y=f(x) aligned & y= x-1 x-2 & y x-2 y=x-1 & (y-1) x=2 y-1 & x=f⁻¹(y)= 2 y-1 y-1 aligned As the function is invertible on the given domain and its inverse can be obtained as above.

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