Final answer:
The domain of a function with an integer in the denominator generally includes all real numbers except those that make the denominator zero. This is because division by zero is undefined in mathematics. Always analyze the denominator to find these values.
Step-by-step explanation:
In mathematics, the domain of a function refers to the set of inputs for which the function is defined. When you have a single integer in the denominator of a function, the domain generally includes all real numbers except for the values that would make the denominator equal to zero. This is because division by zero is undefined in mathematics.
Let's consider an example function f(x) = 1 / (x - 3). For this function, the denominator is zero when x equals 3. So, the domain of this function is all real numbers except 3. We often express it in interval notation as (-∞, 3) U (3, ∞), where U represents the union of the two intervals.
Remember, the main goal is to avoid division by zero, so carefully analyze the denominator and determine the values that may cause this situation.
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