If the function f:[1, ) [1, ) is defined by f(x)=2^ x x-1 , then f^ -1 (x) is
Mathematics · JEE Main · NTA Exams — Sets, Relations and Functions
If the function \(f:[1, \infty) \rightarrow[1, \infty)\) is defined by \(f(x)=2^{x \mid x-1}\), then \(f^{-1}\)(x) is
- \(\left(\frac{1}{2}\right)^{x|x-1|}\)
- \(\frac{1}{2}\left(1+\sqrt{1+4 \log _{2} x}\right)\)
- \(\left[1-\sqrt{1+4 \log _{2} x}\right]\)
- not defined
Answer
(B) 1 2 (1+ 1+4 _ 2 x )
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