Exercises: Terms with Square Roots
What is the domain of definition?
For this task you need the following basic knowledge: Square Roots
Only positive or zero expressions are allowed under the root. So must be positive or zero. becomes zero for .
When we make smaller (so ), then gets negative (which is not good)
When we make larger (so ), then becomes positive (which is what we want).
So is the required condition for obtaining a positive or zero number under the root. Further, is a real number, so
For this task you need the following basic knowledge: Square Roots
Only positive or zero expressions are allowed under the root. So must not be negative. Now, is never negative and if we add , it only becomes "more positive". So any is allowed in the domain of definition, as long as it is a real number:
For this task you need the following basic knowledge: Square Roots
Only positive or zero expressions are allowed under the root. So must not be negative. Further, we cannot divide by zero, which excludes the case , which happens if becomes zero. So only is allowed. This is the case whenever . Further, we know that is a real number.
So the domain of definition of is characterized by
For this task you need the following basic knowledge: Square Roots
Only positive or zero expressions are allowed under the root. So must not be negative. That means, must be larger or equal .
For and , you exactly obtain . This is a "good case"
If is positive, then making larger (so ) will make larger than , which is also a "good case".
Analogously, for negative , making even more negative (so ) will also result in , which is good for our purposes.
However, if -, so , then becomes smaller than 36, which is not good.. So we have to exclude this case.
Further, we know that is a real number. So the domain of definition is given by