The inverse of the function f(x)= 10^ x -10^ -x 10^ x +10^ -x is (Assume that f(x) is…

Mathematics · JEE Main · NTA ExamsSets, Relations and Functions

The inverse of the function \(f(x)=\frac{10^{x}-10^{-x}}{10^{x}+10^{-x}}\) is (Assume that \(f(x)\) is bijective)
  1. \(\log _{10}(2-x)\)
  2. \(\frac{1}{2} \log _{10}\left(\frac{1+x}{1-x}\right)\)
  3. \(\frac{1}{2} \log _{10}(2 x-1)\)
  4. \(\frac{1}{4} \log \left(\frac{2 x}{2-x}\right)\)

Answer

(B) 1 2 _ 10 ( 1+x 1-x )

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