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