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Give the domain of the function defined as follows. f(x)=sqrt(25−x^2)

User Barth
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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].

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User Shekhar Chikara
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