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

Question

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, x 2 - 6 x + 3 = 0, x 2 - 6 x + 9 = 0, x 2 - x + 3 = 0, x 2 - 3 = 0

MARKS App · Accepted Answer

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 - 3 = 0 , x ≠ 0

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