Find the domain of each function...

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Key Concepts

Intersection of Conditions

When a function involves multiple restrictions, such as those imposed by radicals and rational expressions, the final domain is determined by taking the intersection of the individual conditions. This means that only those input values that satisfy every constraint simultaneously are included in the domain.

Denominator Restrictions

In rational functions, any value that makes a denominator equal to zero is excluded from the domain. It is crucial to identify and exclude these values because division by zero is undefined.

Radical Expressions

When a function includes a square root or any even-indexed radical, the expression inside the radical must be greater than or equal to zero to ensure that the output is a real number. This requirement provides an inequality that restricts the domain of the function.

Domain of a Function

The domain of a function is the set of all input values for which the function is defined. Determining the domain involves identifying any restrictions, such as divisions by zero or invalid operations like taking the square root of a negative number, and then expressing the domain as all real numbers that meet these conditions.

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