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CUET · MATHS · PYQ PAPER 2023

If \(A = \mathbb{R} - \left\{\frac{3}{2}\right\}\) and function \(f: A \rightarrow A\) is defined by \(f(x) = \frac{3x-2}{2x-3}\), then

  1. A \(f^{-1}(x) = f(x)\)
  2. B \(f^{-1}(x) = -f(x)\)
  3. C \(f \circ f(x)=-x\)
  4. D \(f^{-1}(x) = \frac{3x+2}{2x+3}\)
Verified Solution

Answer & Solution

Correct Answer

(A) \(f^{-1}(x) = f(x)\)

Step-by-step Solution

Detailed explanation

Let \(y = \frac{3x-2}{2x-3}\). \(y(2x-3) = 3x-2\) \(2xy - 3y = 3x - 2\) \(x(2y - 3) = 3y - 2\) \(x = \frac{3y - 2}{2y - 3}\) \(f^{-1}(x) = \frac{3x - 2}{2x - 3}\) \(f^{-1}(x) = f(x)\)