JEE Main202524 Jan 2025Morning ShiftMathematicsFunctionsActual

Let f(x)= 2^ x+2 +16 2^ 2 x+1 +2^ x+4 +32 . Then the value of 8 (f ( 1 15 )+f ( 2 15 )+ +f ( 59 15 ) ) is equal to

Options

A92
B118
C102
D108

Correct answer

B. 118

Step-by-step solution

aligned & f(x)= 42^x+16 2.2^ 2 x +16.2^x+32 & f(x)= 2 (2^x+4 ) 2^ 2 x +8.2^x+16 & f(x)= 2 2^x+4 & f(4-x)= 2^x 2 (2^x+4 ) & f(x)+f(4-x)= 1 2 aligned So, f ( 1 15 )+ f ( 59 15 )= 1 2 aligned & Similarly =f ( 29 15 )+f ( 31 15 )= 1 2 & f ( 30 15 )=f(2)= 2 2^2+4 = 2 8 = 1 4 & 8 (29 1 2 + 1 4 ) aligned Ans. 118

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