Let f (x) = 2 2x+1 +16 x+4 . Then the value of 8 (f ( 1 ) + f ( 2 ) + \ldots + f ( 59 )) is equal to 2 +2 +32 15 15 15
Step-by-Step Solution
Key Concept: Apply the core result for domains, ranges and functional equations and simplify using the given constraints.
f (x) = 42 + 16 2x x (2) 2.2 + 16.2 + 32 x 2 (2 + 4) f (x) = 2x x 2 + 8.2 + 16 2 f (x) = x 2 + 4 x 2 f (4 - x) = x 2 (2 + 4) 1 f (x) + f (4 - x) = 2 So, f ( 1 15 ) + f ( 59 15 ) = 1 2 29 31 1 Similarly = f ( ) + f ( ) = 15 15 2 30 2 2 1 f ( ) = f (2) = = = 2 15 8 4 2 + 4 1 1 \Rightarrow 8 (29 \times + ) 2 4 Ans. 118
Correct Answer: 2