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NDA 2 2025 Maths, question 90

Topic: Differential calculus

Passage · Q89 to Q90

Consider the function f(x)=10x−10−x10x+10−xf(x)=\frac{10^{x}-10^{-x}}{10^{x}+10^{-x}}.

Q90

What is the inverse of the function?

  1. (a) log⁡10(2x−1)\log _{10}(2x-1)
  2. (b) 12log⁡10(2x−1)\frac{1}{2}\log _{10}(2x-1)
  3. (c) 14log⁡10(2x2−x)\frac{1}{4}\log _{10}\left( \frac{2x}{2-x} \right)
  4. (d) 12log⁡10(1+x1−x)\frac{1}{2}\log _{10}\left( \frac{1+x}{1-x} \right)Correct answer

Solution.

Answer: (d) 12log⁡10(1+x1−x)\frac{1}{2}\log _{10}\left( \frac{1+x}{1-x} \right)

  1. Set y=(10²ˣ−1)/(10²ˣ+1).
  2. Rearranging gives 10²ˣ=(1+y)/(1−y), so x=(1/2)log₁₀[(1+y)/(1−y)].
  3. Thus option (d) is the inverse, whose domain is −1<y<1.