Verified Solution • 2025–26 Session moderate

QJEEM18Mac5ef: JEE Main 2018 Mathematics - Class 11 JEEM18Mac5ef Solution: Let f : A → B be a function defined as f(x) = x − 1 x − 2 ,…

Let f : A → B be a function defined as f(x) = x−1x−2, Where A = R − {2} and B = R − {1}. Then   f   is :

Multiple Choice Options

  • A invertible and f−1(y)= 3y−1y−1
  • B invertible and f−1(y)=2y−1y−1
  • C invertible and f−1(y)=2y+1y−1
  • D not invertible

Step-by-Step Verified Solution

Assume,

y = f(x)

⇒ y = x−1x−2

⇒ yx - 2y = x - 1

⇒ (y - 1)x = 2y - 1

⇒ x = 2y−1y−1 = f -1(y)

As on the given domain the function is invertible and its inverse can be computed as shown above.

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