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If f(x)= 2^ x +2^ -x 2 , then f(x+y) f(x-y) is

Options

  1. A1 4 [f(2 x)-f(2 y)]
  2. B1 2 [f(2 x)-f(2 y)]
  3. C1 4 [f(2 x)+f(2 y)]
  4. D1 2 [f(2 x)+f(2 y)]

Correct answer

D. 1 2 [f(2 x)+f(2 y)]

Step-by-step solution

Given f(x)= 2^ x +2^ -x 2 Now, f(x+y)= 2^ x+y +2^ -x-y 2 and f(x-y)= 2^ x-y +2^ -x+y 2 f(x+y) f(x-y)= (2^ x+y +2^ -x-y ) 2 (2^ x-y +2^ -x+y ) 2 = 2^ 2 x +2^ -2 y +2^ 2 y +2^ -2 x 4 = 1 2 ( 2^ 2 x +2^ -2 x 2 )+ ( 2^ 2 y +2^ -2 y 2 ) = 1 2 f(2 x)+f(2 y)

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