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

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)?

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

Answer 1

f[(a/2)] = sqrt[(1+f(a))/2]

Since f(a)=0, f([(a/2)]=(1/2)√2

Then f[(a/4)] = sqrt{[1+f[(a/2)]/2} = sqrt{[1+(.5√2)]/2} = (0.5)sqrt(2+√2)] = 0.5*sqrt(3.414)=.92

Sorry, I don't get.98 either!