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NCERT Class 12 · Ch 1 Miscellaneous Exercise · Q5

NCERT Class 12 Maths · Chapter 1 Relations And Functions · Miscellaneous Exercise Question 5

Let A={−1,0,1,2}, B={−4,−2,0,2}, f,g:A→B, with f(x)=x²−x and g(x)=2|x−1/2|−1. Are f and g equal? Justify.

💡 Concept Hints

  1. A function on a finite domain can be compared by checking every permitted input.
  2. Write the defining condition carefully and preserve every domain restriction while simplifying.

✅ Step-by-Step Solution

Final Answer: Yes; the value lists are both (2,0,0,2) on A in the stated order.
  1. Compute f(−1)=2, f(0)=0, f(1)=0, f(2)=2. Every output belongs to B.
  2. Compute g(−1)=2(3/2)−1=2, g(0)=2(1/2)−1=0, g(1)=0, g(2)=2.
  3. The domain and codomain are the same, and f(x)=g(x) for each of the four domain elements.
  4. Therefore f=g as functions on A, although the expressions do not agree for all real inputs.

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