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Paragraph: Let f(x) be a function satisfying f(x+y)=f(x) f(y) for all x, y N such that f(1)=2 : Question: What is _ x=1 ^6 2^x f(x) equal to?

Options

  1. A1365
  2. B2730
  3. C4024
  4. D5460

Correct answer

D. 5460

Step-by-step solution

aligned & _ x=1 ^6 2^x f(x)=2 f(1)+2^2 f(2)+2^3 f(3) +2^6 f(6) & =2 .(2)+4 .(4)+8 .(8)+ 64.64 & =4+16+64 6 terms & = 4 (4^6-1 ) 4-1 = 4 4095 3 =5460 aligned

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