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NDA 1 2024 Maths, question 73

Topic: Algebra

Q73

If f(x)=ax−bf(x)=ax-b and g(x)=cx+dg(x)=cx+d are such that f(g(x))=g(f(x))f(g(x))=g(f(x)), then which one of the following holds ?

  1. (a) f(d)=g(b)f(d)=g(b)
  2. (b) f(b)+g(d)=0f(b)+g(d)=0
  3. (c) f(a)+g(c)=2af(a)+g(c)=2a
  4. (d) f(d)+g(b)=2df(d)+g(b)=2dCorrect answer

Solution.

Answer: (d) f(d)+g(b)=2df(d)+g(b)=2d

  1. Equating the constant terms in the two compositions gives ad − b = d − bc.
  2. Hence ad + bc = d + b.
  3. Therefore f(d) + g(b) = ad − b + bc + d = 2d.