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AP EAMCET202420 May 2024Evening ShiftMathematicsFunctionsActual

f: R R is defined by f(x+y)=f(x)+12 y, x, y R If f(1)=6 , then _ r=1 ^n f(r)=

Options

  1. An^2
  2. B5 n^2
  3. C6 n^2
  4. D3 n(n+1) 2

Correct answer

C. 6 n^2

Step-by-step solution

f^ (x)=12 , Given f(1)=6f(2)=f(1)+12(1)=6+12=18 Similarly, f(3)=30 ; f(4)=42 aligned & _ r=1 ^n f(r)=6+18+30+42 n terms & =6(1+3+5+7 . n terms )=6 . n^2 aligned

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