"Determine the definition set of the root term"

What is the definition set?

• The definition set indicates for which x-values ​​of a function term there are associated y-values. The values ​​for which the term would contain an invalid arithmetic expression are excluded from the definition set.
• Fractions are an example of this. With a fraction term, the x-value cannot be a number where the denominator would become 0.
• The definition set is not only limited for fractions, even that of a root term does not always contain the entire range of real numbers. There must be no negative numbers under the root.

This is how you determine the domain of a root term

The set of definitions of a square root term is restricted by the fact that there are no negative terms under the root Counting are allowed to stand. With this condition you can easily determine the possible x-values.

1. Take the term that is under the root and set it equal to zero.


Definition set - what is it?

You will encounter the definition set as a technical term in mathematics, mostly in ...

2. Now solve the term for x. These values ​​are definitely included in the definition set.
3. Now choose a number that is slightly smaller than the smallest x-value that results in 0 for the root term and insert this into the root term. If the result is negative, all values ​​that are smaller than this smallest x-value fall out of the definition set.
4. Do you have several x-values ​​that result in 0 for the root term? Then insert a value that lies between these values ​​in the term and also check here whether the result is positive or negative. If it is negative, all values ​​between the x values ​​that result in 0 fall out of the definition range.
5. Now also check a value that is larger than the largest calculated x-value.
6. When you have checked all of this, you will know which values ​​do not give a valid result for the root term. This allows you to restrict the definition set accordingly.

If it is a term of the third root, negative values ​​are also possible. So you don't have to make any restrictions here.