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BITSAT2016MathematicsFunctionsActual

Let f(x)= a x+b c x+d , then fof (x)=x, provided that:

Options

  1. Ad =- a
  2. Bd = a
  3. Ca=b=1
  4. Da=b=c=d=1

Correct answer

A. d =- a

Step-by-step solution

f(x)= a x+b c x+d fof (x)= a a x+b c x+d +b c a x+b c x+d +d a² x+a b+b c x+b d a c x+b c+c d x+d² =x (a c+d c) x²+ (b c+d²-b c-a² ) x-a b-b d=0, x R (a+d) c=0, d²-a²=0 and (a+d) b=0 a+d=0

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