Strange recurrence relation

Question

I am trying to solve $f(n)=f( \sqrt{n}$) .Seems very strange to me, the iterator (iterator means how many steps we need to take in order to reach 1 ) then the steps are indeed $\lg\lg(n$) but how should I proceed? I found the answer it is $f(n)$=$\Theta(\lg\lg(n))$,but why?

Answer 1

Hint: Master's theorem. ${ }$