Final answer:
The domain of the function f(x)=(x+3)/(x²-9) is all real numbers except x = -3 and x = 3, while the domain of g(x)=(x²)/(x+4) is all real numbers except x = -4.
Step-by-step explanation:
The domain of a function is the set of all possible input values for which the function is defined. To find the domain of a rational function like f(x)=(x+3)/(x²-9), we need to determine the values of x that make the denominator equal to zero. In this case, the denominator x²-9 is equal to zero when x = -3 or x = 3. Therefore, the domain of f(x) is all real numbers except x = -3 and x = 3.
Similarly, for g(x)=(x²)/(x+4), the denominator x+4 is equal to zero when x = -4. Therefore, the domain of g(x) is all real numbers except x = -4.
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