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AP EAMCET20227 Jul 2022Morning ShiftMathematicsFunctionsActual

If a function f satisfies f(x+1)+f(x-1)= 2 f(x) , then f(x+2)+f(x-2)=

Options

  1. A2 f(x)
  2. Bf(x+1)-f(x-1)
  3. C4 f(x)
  4. D0

Correct answer

D. 0

Step-by-step solution

Given, f(x+1)+f(x-1)= 2 f(x) ...(i) Replace x by x+1f(x+2)+f(x)= 2 f(x+1) ...(ii) Replace x by x-1 in Eq. (i), f(x)+f(x-2)= 2 f(x-1) ...(iii) On adding Eqs. (ii) and (iii), aligned f(x+2)+f(x-2) & +2 f(x) = & 2 [f(x+1)+f(x-1)] aligned f(x+2)+f(x-2)=0

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