I wonder what went wrong here: Find the domain of f(x)=sqrt(1-sqrt(1-x2)) So of course the term under the radical must be greater than or equal to zero. For neatness I ignore the equal part. 1-sqrt(1-x2)>0 1>sqrt(1-x2) both left and right are positive, so 1>1-x2 x2>0 But it seems to me that the domain is actually [-1,1] You can do this alternatively by finding the domain of the innermost radical, which is [-1,1], and intersecting it with the set of all x such that sqrt(1-x2) is in the domain of h(y)=sqrt(1-y). Since sqrt(1-x^2)>=0 for all x in its domain, the intersection is just [-1,1]. So what happened wrong with the first approach?