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NDA 1 2025 Maths, question 89

Topic: Differential calculus

Passage · Q89 to Q90

Let the function f(x)=x2−1f(x) = x^{2} - 1.

Q89

What is lim⁡x→1{f∘f(x)}\lim_{x \rightarrow 1}{\{ f \circ f(x)\}} equal to?

  1. (a) -1Correct answer
  2. (b) 0
  3. (c) 1
  4. (d) 2

Solution.

Answer: (a) -1

  1. The composition is f(f(x))=(x2−1)2−1f\left( f(x) \right) = \left( x^{2} - 1 \right)^{2} - 1.
  2. It is a polynomial and hence continuous, so direct substitution gives (1−1)2−1=−1(1 - 1)^{2} - 1 = - 1.