Answer :

**Given:**

Domain: These are the values of x for which f(x) is defined.

from the given f(x) we can say that, f(x) should be real and for that,

9 - x^{2} ≥ 0 [Since a value less than 0 will give an imaginary value]

(3 + x)(3 - x) ≥ 0

Now there are two critical points, x = + 3 and x = - 3

Taking a value less than - 3 and putting in the expression we get,

(3 - 5)(3 + 5) = -ve value and thus

Plotting these on number line we get,

Since, f(x) is defined for all real numbers that are greater than or equal to -3 and less than or equal to 3, **the domain of f(x) is [-3, 3].**

From the f(x) we can see that, the values obtained will only be positive and can be any positive number less than 3.

Hence,

**Range of f(x) = [0, 3)**

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