Final answer:
The domain of the function f(x)=sqrt(25−x^2) is the interval [-5, 5].
Step-by-step explanation:
The domain of the function f(x)=sqrt(25−x^2) can be determined by finding the values of x for which the function is defined. The square root function is defined only for non-negative values. Therefore, we need to find the values of x that make the expression inside the square root non-negative:
25−x^2 ≥ 0
This inequality represents the values of x that satisfy the domain of the function. To solve it, we can factor the expression as (5+x)(5-x) ≥ 0. Setting each factor greater than or equal to zero, we get x ≤ 5 and x ≥ -5.
Therefore, the domain of the function is the interval [-5, 5].
Learn more about Domain of a function