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MHT CET202313 May 2023Morning ShiftMathematicsFunctionsActual

If 3 f (x)- f ( 1 x )=8 ₂ x^3, x>0 , then f (2), f (4) f (8) are in

Options

  1. AA.P.
  2. BG.P.
  3. CH.P.
  4. DArithmetico Geometric Progression.

Correct answer

A. A.P.

Step-by-step solution

aligned & 3 f(x)-f ( 1 x )=8 ₂ x^3 & 3 f ( 1 x )- f (x)=8 ₂ ( 1 x )^3 . aligned From (i) and (ii), we get aligned & 8 f (x)=24 ₂ x^3+8 ₂ ( 1 x )^3 & 8 f (x)=72 ₂ x-24 ₂ x & 8 f (x)=48 ₂ x & f (x)=6 ₂ x aligned array ll & f^ (2)=6 ₂ 2=6 & f^ (4)=6 ₂ 4=12 & f^ ( (8)=6 ₂ 8=18 & f(2), f(4), f(8) are in A.P. array

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