When a function is defined, it is often the case that the domain
of is not explicitly stated.
In such a case we will consider the domain to be the set of real
numbers so that the value is also a real number.
This is called the *implied domain* of .
For example,
is
the implied domain of square root function
.

**Equations of a semicircle.**
By the Pythagorean theorem the point on the semicircle with
radius must satisfy

(1) |

By solving (1) in terms of we obtain . Considering a semicircle for , we obtain an equation of the semicircle as follows.

**Square root function.**
A function is called a *square root function* if

Department of Mathematics