Find the domain of the function  f(x)=9−x2x2−4

We must have 9−x2≥0 or  x2≤9-------1 and x2−4>0 or  x2>4------2 From (i), x∈[−3,3]------3 and from (ii), x∈(−∞,−2)∪(2,∞)------4 From (3) and (4), we get x∈[−3,−2)∪(2,3]