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
- A \(f^{-1}(x) = f(x)\)
- B \(f^{-1}(x) = -f(x)\)
- C \(f \circ f(x)=-x\)
- D \(f^{-1}(x) = \frac{3x+2}{2x+3}\)
Answer & Solution
Correct Answer
(A) \(f^{-1}(x) = f(x)\)
Step-by-step Solution
Detailed explanation
Let \(y = \frac{3x-2}{2x-3}\). \(y(2x-3) = 3x-2\) \(2xy - 3y = 3x - 2\) \(x(2y - 3) = 3y - 2\) \(x = \frac{3y - 2}{2y - 3}\) \(f^{-1}(x) = \frac{3x - 2}{2x - 3}\) \(f^{-1}(x) = f(x)\)
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