Example 4
{(x,y):y^2＝x}
[This should be read , "The set of all ordered pairs (x,y) such that y^2=x."〕This is a relation but not a function because , for each nonnegative number that is substituted for x , there are two values for y . For example , x = 4, y = +2, or y = -2.Domain = {all nonnegative real numbers }. Range = {all real numbers }.

The expressions f = {(x,y):y = x^2} and f(x) = x^2 both name the same function ; f is the rule that pairs any number with its square . Thus , f(x) = x^2, f(a) = a^2w, f(z) = z^2 all name the same function . The symbol f(2) is the value of the function f when x = 2. Thus , f(2) = 4.

EXERCISES
⒈If {(3,2),(4,2),(3,1),(7,1),(2,3)} is to be afunction , which one of the following must be removed from the set ?
(A) (3,2)
(B) (4,2)
(C) (2,3)
(D) (7,1)
(E) none of the above

⒉For f(x) = 3x^2+4, g(x) = 2, and h {1,1),(2,1),(3,2)},
(A) f is the only function
(B) h is the only function
(C) f and g are the only functions
(D) g and h are the only functions
(E) f,g,and h are all functions

COMBINING FUNCTIONS
If f and g name two functions , the following rules apply :
(f+g)(x) = f(x)+g(x)
(f-g)(x) = f(x)-g(x)
(f · g)(x) = f(x) · g(x)
(f/g)(x) = f(x)/g(x)
if and only if g(x) ≠ 0
(f ○ g)(x) = f(g(x))
(this is called the composition of functions).