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MHT CET202525 Apr 2025Morning ShiftMathematicsFunctionsActual

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

Options

  1. A2 f (x)
  2. B3 f (x)
  3. C4 f (x)
  4. D- f (x)

Correct answer

B. 3 f (x)

Step-by-step solution

To compute the composition (f g)(x) = f(g(x)) , substitute g(x) into f : f(g(x)) = ( 1 + g(x) 1 - g(x) ) Given g(x) = 3x + x^3 1 + 3x^2 , we find: 1 + g(x) = (1+x)^3 1+3x^2 , 1 - g(x) = (1-x)^3 1+3x^2 Substituting these into the expression: f(g(x)) = ( (1+x)^3/(1+3x^2) (1-x)^3/(1+3x^2) ) = ( (1+x)^3 (1-x)^3 ) = ( ( 1+x 1-x )^3 ) Apply the logarithmic identity: f(g(x)) = 3 ( 1+x 1-x ) = 3f(x) This confirms option B is correct.

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