Question

find the domain and range of:
the square root of 25-x^2

Answer 1

f(x)=√(25-x²)
For f(x) to be real, we require that the expression 25-x² be non-negative, i.e.
25-x²≥0 ....(1)
(1) is satisfied when
|x|≤5,
or x∈[-5,5] which is exactly the domain of f(x).
The range of f(x) varies from 0 when x=±5 to 5 when x=0.