Does each rule specify a function Let x be the number of boy

Does each rule specify a function?

Let x be the number of boys in family. Let f(x) be the number of people in a family with x boys.

Let y be the number of children in a family. Let g(y) be the number of children in that family that are boys.

Solution

A function relates each element of a given set ( domain of the function )with exactly one element of another set ( co-domain or range of the function). A function is thus subject to the rules that it must define a definite output for every possible input value and it has only one relationship for each input value. Functions are generally represented by a rule where the dependent variable, y, is expressed in terms of the independent variable, x.

However, every rule does not specify a function. For example, a rule that relates a number to its square root, without specifying whether the square root is positive or negative, does not specify a function.