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AP EAMCET202120 Aug 2021Morning ShiftMathematicsFunctionsActual

Let f ( x ) = x 3 and g ( x ) = 3 x , then the quadratic equation whose roots are solutions of the equation ( f ∘ g ) ( x ) = ( g ∘ f ) ( x ) ( for x ≠ 0 ) is

Options

  1. Ax 2 - 6 x + 3 = 0
  2. Bx 2 - 6 x + 9 = 0
  3. Cx 2 - x + 3 = 0
  4. Dx 2 - 3 = 0

Correct answer

D. x 2 - 3 = 0

Step-by-step solution

Let f ( x ) = x 3 and g ( x ) = 3 x ( f ∘ g ) ( x ) = ( g ∘ f ) ( x ) (for x ≠ 0 ) ( f ∘   g   ) ( x )   =   f (   g   ( x )   )   =   f (   3 x )   =   3 3 x ( g   ∘   f ) ( x )   =   g (   f   ( x )   )   =   g (   x 3 )   =   3 x 3 Equating the powers with same base x 3   -   3 x   =   0 x ( x 2   -   3 )   =   0 x 2   -

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