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MHT CET202312 May 2023Morning ShiftMathematicsFunctionsActual

If g (x)=1+ x and f ( g (x))=3+2 x +x , then f ( f (x)) is

Options

  1. Ax^2+4 x+6
  2. Bx^4+x^2+6
  3. Cx^2+x+6
  4. Dx^4+4 x^2+6

Correct answer

D. x^4+4 x^2+6

Step-by-step solution

aligned & g(x)=1+ x and f ( g (x))=3+2 x +x & f ( g (x))= [( x )^2+2 x +1 ]+2 & =( x +1)^2+2 & =[ g (x)]^2+2 & f (x)=x^2+2 & f ( f (x))= (x^2+2 )^2+2=x^4+4 x^2+6 & aligned

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