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Chapter 2: Problem 103

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, consider all possible 'x' values. Identify any values that may cause the function to be undefined, such as division by zero or getting the square root of a negative number. These values have to be excluded from the domain.

Step by step solution

01

- Understanding Domain

Domain represents all possible values that can be put into the function. Any value that results in an undefined output is not considered part of the domain. In algebraic terms, the domain is all the permissible values of 'x' in a function.
02

- Identifying Restrictions

Look for operations that can restrict the domain - division by zero and taking the square root (or even root) of a negative number. Any value of 'x' that may cause a division by zero or the square root of a negative number should be excluded from the domain.
03

- Test and Exclude Undefined Values

Test the values. For instance, if your function contains a denominator, set the denominator equal to zero and solve for 'x'. The solutions will give you the values to exclude from the domain. If the function involves a square root, ensure that the values of 'x' under the square root sign aren't negative.
04

- Formulate the Domain of the Function

After identifying and excluding the values that make the function undefined, list out the remaining possible values of 'x'. This list is the domain of the function.

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Most popular questions from this chapter

Use a graphing utility to graph each circle whoseequation is given. Use a square setting for the viewing window. $$x^{2}+10 x+y^{2}-4 y-20=0$$

Exercises \(103-105\) will help you prepare for the material covered in the next section. Use a rectangular coordinate system to graph the circle with center \((1,-1)\) and radius 1.

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