Find the range .

Question

f(x)=1⁄√9-x²

Domain=  (-3,3)

Sol.1⁄√9-(±3²)=1/0=Not defined

1/√9-(±2²)=1/√5

1⁄√9-(±1²)=1/√8

1⁄√9-0=1/√9=1/3

Then ,why range is =[1/3,∞) ? Why the answer is ≠[1/3,1/√5]?

 

Answer 1

Because there are vertical asymptotes at x=-3,3 and the function

tends towards ∞ as they're approached (from within the domain).