@@Kairav-lb8fh 1. The square root is defined for positive values: 9-x^2 ≥ 0 ==> -3≤x≤3 ==> X Є [-3,3] 2. The minimum value for sqrt(9-x^2) is when x=3 and the minimum value is when x=0: Since sqrt(9-3^2)=0 and sqrt(9-0^2) = 3 then the range is [0,3]
You can understand in this way as well: Given that f(x)=√9−x2 The domain of the given function is x∈[−3,3] ⇒−3≤x≤3 ⇒0≤x2≤9 ⇒−9≤−x2≤0 ⇒0≤9−x2≤9 ⇒0≤√9−x2≤3 ⇒0≤f(x)≤3 The range of the function is [0,3].
