New functions are often formed from simpler ones, say f(x) and g (x), by the algebraic processes of addition, subtraction, multiplication and division.
When such functions are formed, their domains of definition comprise those
values of x which are common to the domain of definition (a , b) associated
with f(x) and the domain of definition (a , b ) associated with g(x ). The
domain of definition of the combined functions is illustrated diagrammati-
cally in Fig. 24.