CUET · MATHS · PYQ PAPER 2023
Let \(f: R -\left\{\frac{3}{5}\right\} \rightarrow R\) be defined by \(f(x)=\frac{3 x+2}{5 x-3}\), then
- A \(f^{-1}(x)=f(x)\)
- B \(f^{-1}(x)=-f(x)\)
- C \((f \circ f)(x)=x^2\)
- D \(f^{-1}|x|=\frac{1}{19} f(x)\)
Answer & Solution
Correct Answer
(A) \(f^{-1}(x)=f(x)\)
Step-by-step Solution
Detailed explanation
Let \(y = f(x)\). \(y = \frac{3x+2}{5x-3}\) Swap \(x\) and \(y\): \(x = \frac{3y+2}{5y-3}\) Solve for \(y\): \(x(5y-3) = 3y+2\) \(5xy - 3x = 3y+2\) \(5xy - 3y = 3x+2\) \(y(5x-3) = 3x+2\) \(f^{-1}(x) = y = \frac{3x+2}{5x-3}\) Therefore, \(f^{-1}(x) = f(x)\)
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