Let the function f : 0 , 1 → ℝ be defined by f x = 4 x 4 x + 2 . Then the value of f 1 40 + f 2 40 + f 3 40 + ⋯ + f 39 40 - f 1 2 is_________

Question

Let the function f : 0 , 1 &#8594; &#8477; be defined by f x = 4 x 4 x + 2 . Then the value of f 1 40 + f 2 40 + f 3 40 + &#8943; + f 39 40 - f 1 2 is_________

Aicharya · Accepted Answer

f x = 4 x 4 x + 2 , &#160;&#160; f 1 - x = 4 1 - x 4 1 - x + 2 = 2 4 x + 2 &#8658; f x + f 1 - x = 1 f 1 40 + f 2 40 + &#8230; . . + f 39 40 - f 1 2 = f 1 40 + f 39 40 + f 2 40 + f 38 40 + . . . . . f 19 40 + f 21 40 + f 20 40 - f 1 2 = 19 .

Let the function f : 0 , 1 → ℝ be defined by f x = 4 x 4 x + 2 . Then the value of f 1 40 + f 2…

Solution

Let the function f : 0 , 1 &#8594; &#8477; be defined by f x = 4 x 4 x + 2 . Then the value of f 1 40 + f 2…

Solution

Let the function f : 0 , 1 → ℝ be defined by f x = 4 x 4 x + 2 . Then the value of f 1 40 + f 2…