Determine the domain of each function....

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Key Concepts

Domain of a Function

The domain of a function consists of all the possible input values (typically represented by x) for which the function is defined. Understanding the domain is essential because it determines the set of values that you can substitute into the function without causing mathematical issues, such as division by zero or taking the square root of a negative number.

Rational Functions

Rational functions are functions expressed as the ratio of two polynomials. When analyzing these functions, it is important to consider the values that make the denominator zero, as these values are excluded from the domain. This approach ensures that the function remains defined and avoids undefined operations like division by zero.

Avoiding Division by Zero

In the context of rational functions, division by zero is a critical issue because it results in undefined expressions. When determining the domain, any value of x that causes the denominator to become zero must be excluded from the domain. Analyzing the denominator in a rational function helps in identifying such forbidden values.

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