A function f has the property that f(x/2) = Sqrt((1 + f(x))/2) for 0 <= x <= 1. If f(a) = 0 where 0 <= a <=1, what is the value of f(a/4)?

Question

Apparently the answer is 0.98, but I have no idea how to get that.

Answer 1

f(x/2) = √{[1 + f(x)]/2}

 

f(a/4) = f((a/2)/2)

 

Note that a/2 is in the place of x, so

 

f(a/4) = √{[1 + f(a/2)]/2}

 

f(a/2) = √{[1 + f(a)]/2} = √{[1 + 0]/2} = √(1/2)

 

Plug the result for f(a/2) into the equation for f(a/4) and get

 

f(a/4) = √{[1 + f(a/2)]/2} = √{[1 + √(1/2)]/2} = 0.9238795...

 

Are you sure the correct answer is 0.98?