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NDA 2 2025 Maths, question 89

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}}.

Q89

What is f∘f∘f∘f∘f(0)f\circ f\circ f\circ f\circ f(0) equal to?

  1. (a) 00Correct answer
  2. (b) 11
  3. (c) 55
  4. (d) 1010

Solution.

Answer: (a) 00

  1. f(0)=(1−1)/(1+1)=0.
  2. Every further application of f therefore keeps the value at zero, so the fivefold composition is 0.