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Find the domain of f(x)=sqrt(1-sqrt(1-x

^{2}))

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-x

^{2})>0

1>sqrt(1-x

^{2})

both left and right are positive, so

1>1-x

^{2}

x

^{2}>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-x

^{2}) 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?