UPSC NDA Math Model Paper 2

Given function is (x)=√(16−x2)
The domain of a function f(x) is the set of all values for which the function is defined, and the range of the function is the set of all values that f takes.
For domain, f(x) ≥ 0
⇒16−x2≥0
⇒16≥x2
⇒x2≤16
⇒−4≤x≤4 Hence, domain of f(x)=[−4,4]
For Range,
f(x) is maximum at x = 0 i.e. f(0) = 4
f(x) is minimum at x = 4 i.e. f(4) = 0
Hence, Range of f(x) = [0, 4]
Hence, the domain and range of the function (x) = of the function (x)=√(16−x2) are [-4, 4], [0, 4].