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AP EAMCET202125 Aug 2021Morning ShiftMathematicsFunctionsActual

The inverse of the function y= 10^x-10^ -x 10^x+10^ -x is

Options

  1. A1 2 ₁₀ ( 1+x 1-x )
  2. B1 2 ₁₀ ( 2+x 2-x )
  3. C1 2 ₁₀ ( 1-x 1+x )
  4. D1 2 ₁₀ ( 2-x 2+x )

Correct answer

A. 1 2 ₁₀ ( 1+x 1-x )

Step-by-step solution

We have, array rlrl y & & = 10^x-10^ -x 10^x+10^ -x y & = 10^ 2 x -1 10^ 2 x +1 10^ 2 x y+y & =10^ 2 x -1 10^ 2 x (y-1) & =-(y+1) & 10^ 2 x & = y+1 1-y & 2 x & = ₁₀ y+1 1-y x & = 1 2 ₁₀ ( 1+y 1-y ) & f⁻¹(x) & = 1 2 ₁₀ ( 1+x 1-x ) array

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