- #1
StephenPrivitera
- 363
- 0
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?
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?