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Chapter 8: Problem 67

If a function is defined by an equation, explain how to find its domain.

Short Answer

Expert verified
To find the domain of a function defined by an equation, identify the type of function, understand each type's constraints on its domain, find any exclusions based on these constraints, and then the domain is all real values that do not violate these exclusions.

Step by step solution

01

- Identify the Function Type

The first step is to identify the type of function you're dealing with. Different types of functions have different rules for their domains. The common types include linear, quadratic, rational, radical, and trigonometric functions.
02

- Recognize Function Constraints

Next, evaluate the constraints each type of function has on its domain. For instance, for rational functions, where the function is a fraction with variables in the denominator, the denominator can't equal to zero since division by zero is undefined. Therefore, you need to find the values of x at which denominator is zero and exclude these from the domain.
03

- Find Possible Exclusions

For square root or radical functions, the expression under the square root sign (radicand) needs to be greater than or equal to zero, because square roots of negative numbers are not real. Therefore, set the radicand greater than or equal to zero and solve for x to find the domain.
04

- Deciding the Domain

Having identified the function and its constraints, all real values that do not violate these restrictions make up the domain of the function.

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