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NDA 2 2024 Maths, question 72

Topic: Algebra

Q72

If f(x)=4x+1f(x)=4x+1 and g(x)=kx+2g(x)=kx+2 such that f∘g(x)=g∘f(x)f\circ g(x)=g\circ f(x), then what is the value of kk?

  1. (a) 77Correct answer
  2. (b) 55
  3. (c) 44
  4. (d) 33

Solution.

Answer: (a) 77

  1. Compute both compositions: f(g(x))=4kx+9, while g(f(x))=4kx+k+2.
  2. Equality for all x requires k+2=9, giving k=7.
  3. Their variable coefficients already agree.