Question
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_________
JEE Advanced
Mathematics
Functions
2020
JEE Advanced 2020 (Paper 2)
JEE Advanced Mathematics Question (2020) — Solution
Options
- A. A
- B. B
- C. C
- D. D
Answer
A. A
Step-by-step solution
f x = 4 x 4 x + 2 ,    f 1 - x = 4 1 - x 4 1 - x + 2 = 2 4 x + 2 ⇒ f x + f 1 - x = 1 f 1 40 + f 2 40 + … . . + 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 .
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