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MHT CET202523 Apr 2025Morning ShiftMathematicsFunctionsActual

If f (x)=3 x +10, ~g (x)=x^2-1 , then ( fog )⁻¹(x)=

Options

  1. A( x-7 3 )
  2. B( x-7 3 )^ 1 2
  3. C( x-7 3 )^ 1 3
  4. D( 3 x-7 )^ 3 2

Correct answer

B. ( x-7 3 )^ 1 2

Step-by-step solution

To determine (f g)⁻¹(x) , the composite function (f g)(x) must first be found, then inverted. Given f(x) = 3x + 10 and g(x) = x^2 - 1 , the composition is: (f g)(x) = f(g(x)) = 3(x^2 - 1) + 10 = 3x^2 + 7 Let y = (f g)(x) = 3x^2 + 7 . Interchanging x and y and solving for y : x = 3y^2 + 7 y^2 = x - 7 3 y = x - 7 3 Since the options only include the principal root, we take: (f g)⁻¹(x) = ( x - 7 3 )^ 1 2 This corresponds to option B .

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