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Let f be a quadratic polynomial such that f(-1-x)=f(-1+x), x R . If (f(1)-5)^2+(f(-1)-1)^2=f^ (-1) , then which of the following is(are) equal to unity? (where [ ] denotes greatest integer function.)

Options

  1. A[ ⁻¹ f(x) ] , wherever defined
  2. B[ sgn (f(x))]
  3. C[ ⁻¹ 1 f(x) ]
  4. D[ ⁻¹ [ 1 2^ f(x) ] ]

Correct answer

D. [ ⁻¹ [ 1 2^ f(x) ] ]

Step-by-step solution

f(-1-x)=f(-1+x) f(x) is symmetrical w.r.t. line x=-1 . f(x)=a(x+1)^2+bf^ (-1)=0 f(1)=5 and f(-1)=1 aligned & b=1, a=1 & f(x)=(x+1)^2+1=x^2+2 x+2 aligned

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