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For f(x)=(x+2)/(x^(2)-9), find the domain and write it in interval notation.

User PhilDin
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Final answer:

The domain of the given function is all real numbers except 3 and -3, which can be written in interval notation as (-∞, -3) ∪ (-3, 3) ∪ (3, ∞).

Step-by-step explanation:

The domain of a function is the set of all possible values of the independent variable for which the function is defined.

In this case, the denominator of the given function cannot be equal to zero because division by zero is undefined. Therefore, we need to find the values of x that make the denominator equal to zero.

The denominator x^2 - 9 can be factored as (x - 3)(x + 3), which means that x cannot be equal to 3 or -3. These values would make the denominator equal to zero.

So, the domain of the function is all real numbers except 3 and -3.

In interval notation, the domain can be written as (-∞, -3) ∪ (-3, 3) ∪ (3, ∞).

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