Answer
a) For all $(x,y,z)$ such that $x^2+y^2+z^2 \le 4$
b) For all $(x,y,z)$ such that $x^2+y^2+z^2 \ge 9$ except when $x^2+y^2+z^2=25$
Work Step by Step
a) We can not take the square root of a negative value. Hence, $4-x^2-y^2-z^2\ge 0$. Thus, for all (x,y,z) such that $ x^2+y^2+z^2 \le 4$
b) There must not be zero in the denominator. Also, we can not take the square root of a negative number.
Thus, $x^2+y^2+z^2-9\ge 0$
And, $4-\sqrt{x^2+y^2+z^2-9}\ne 0$
So, for all $(x,y,z )$ such that $ x^2+y^2+z^2 \ge 9$ except when $x^2+y^2+z^2=25$
