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f(x+a)= 1/2 + sqrt( f(x)-(f(x))^2 ) holds for all x. Prove that the function is periodic

 f(x+a)= 1/2 + sqrt(f(x)-(f(x))^2) holds for all x. Prove that the function is periodic

Grade:upto college level

1 Answers

Parvez ali
askIITians Faculty 47 Points
9 years ago
f(x+a)= 1/2 + sqrt(f(x)-(f(x))^2)
thus f(x+a)>1/2,
f(x+2a)= 1/2 + sqrt(f(x+a)-(f(x+a))^2)
now see the image for further calculations
147-309_140222-143006.jpg

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