What is the domain of the function?
The domain of a function represents all the possible input values for which the function is defined
The domain of a function represents all the possible input values for which the function is defined. In other words, it is the set of all real numbers that the independent variable (usually denoted by x) can take.
To determine the domain of a function, you need to consider any restrictions or limitations that might exist. Here are some common cases to analyze:
1. Rational functions: These functions contain variables in the denominator. To find the domain, you must ensure that the denominator is not equal to zero. Thus, the domain will be all real numbers except for the values that would make the denominator zero.
2. Square root functions: These functions contain square roots with an expression under them. To find the domain, you need to ensure that the expression under the square root is greater than or equal to zero. This is because taking the square root of negative numbers is not defined in the real number system. Thus, the domain will be all the values for which the expression under the square root is greater than or equal to zero.
3. Absolute value functions: These functions involve the absolute value of a variable. The domain for these functions is all real numbers because there are no restrictions or limitations.
4. Piecewise-defined functions: These functions have different rules or expressions for specific intervals or ranges of the independent variable. To determine the domain, you need to consider the individual rules within each interval and find the intersection (common values) of the domains for each rule.
5. Exponential functions: These functions involve variables as exponents. The domain for these functions is all real numbers because there are no restrictions or limitations.
It is important to note that these are just some common cases, and the domain can vary based on the specific function you are working with. Any additional restrictions, such as the context of the problem or the given conditions, should also be considered when finding the domain.
By analyzing the properties and restrictions of the function, you can determine the appropriate domain for any given function.
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