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MHT CET202415 May 2024Morning ShiftMathematicsFunctionsActual

Let f (x)=(x+1)^2-1, x -1 , then the set x / f (x)= f ⁻¹(x) is

Options

  1. A0,1,-1
  2. B0,-1
  3. C0,-1, -3+ i 3 2 , -3- i 3 2 . , where . i = -1

Correct answer

B. 0,-1

Step-by-step solution

aligned & f (x)= f ⁻¹(x) & f ( f (x))=x & ( f (x)+1)^2-1=x & [(x+1)^2-1+1 ]^2-1=x & (x+1)^4-1=x & (x+1)^4-(x+1)=0 & (x+1) [(x+1)^3-1 ]=0 & x+1=0 or (x+1)^3=1 & x=-1 or x=0 aligned

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