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AP EAMCET202119 Aug 2021Morning ShiftMathematicsFunctionsActual

Given the function f ( x ) = a x + a - x 2 , ( a > 2 ) then f ( x + y ) + f ( x - y ) is equal to

Options

  1. Af ( x ) − f ( y )
  2. Bf ( y )
  3. C2 f ( x ) f ( y )
  4. Df ( x ) f ( y )

Correct answer

C. 2 f ( x ) f ( y )

Step-by-step solution

Given that, f ( x ) = a x + a - x 2 ,   a > 2     . . . . ( i ) ⇒ f x + y = a x + y + a - x + y 2 and f x - y = a x - y + a - ( x - y ) 2 Now, f ( x + y ) + f ( x - y ) = a x + y + a - x - y 2 + a x - y + a - x + y 2 = a y a x + a - x 2 + a - y a x + a - x 2 = a y · f ( x ) + a - y · f ( x ) [from ( i ) ] = 2 · f ( x ) · a y + a - y 2 = 2 · f ( x ) · f ( y )

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