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AP EAMCET202021 Sep 2020Morning ShiftMathematicsFunctionsActual

If (f: R R ) is defined as (f(x)= 2020^x 2020^x+ 2020 ), ( x R ), then ( _ r=1 ⁴⁰³⁹ 2 f ( r 4040 )= )

Options

  1. A4040
  2. B4039
  3. C2020
  4. D1010

Correct answer

B. 4039

Step-by-step solution

The given function (f: R R ) is define as ( aligned & f(x)= 2020^x 2020^x+ 2020 , x R & f(1-x)+f(x)= 2020 2020 + 2020^x + 2020^x 2020^x+ 2020 =1 & 2 _ r=1 ⁴⁰³⁹ f ( r 4040 )=2 & [ f ( 1 4040 )+f ( 4039 4040 ) + f ( 2 4040 )+f ( 4038 4040 ) ] .+ .+ f ( 2019 4040 )+f ( 2021 4040 ) +f ( 2020 4040 ) ] & =2 [2019+f ( 1 2 ) ]=2 [2019+ 1 2 ] f ( 1 2 )= 1 2 & =4039 aligned ) Hence, option (b) is correct.

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