TS EAMCET · Maths · Functions
If \(f:[1, \infty) \rightarrow[0, \infty)\) is given by \(f(x)=x-\frac{1}{x}\), then \(f^{-1}(x)=\)
- A \(x+\sqrt{x^2+4}\)
- B \(\frac{x}{x^2-1}\)
- C \(\frac{1}{2}\left[x+\sqrt{x^2+4}\right]\)
- D \(\frac{1}{2}\left[x-\sqrt{x^2+4}\right]\)
Answer & Solution
Correct Answer
(C) \(\frac{1}{2}\left[x+\sqrt{x^2+4}\right]\)
Step-by-step Solution
Detailed explanation
We have, \(f(x)=x-\frac{1}{x}\) \[ \begin{aligned} f\left(f^{-1}(x)\right) & =f^{-1}(x)-\frac{1}{f^{-1}(x)} \\ x & =\frac{\left(f^{-1} x\right)^2-1}{f^{-1}(x)} \end{aligned} \]…
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