Functions
-Def.: let two sets H and K be given. If we assign an element of set K to each element of H, then this assignment is called the function.
-Def.: set H is the domain of the function.
-Def.: set K is the range of the function.
-The functions will be denoted by letters, generally by f, g, h...
-It is common to denote the domain of the function f by Df and the range of the function f by Rf.If we do not declare the domain separately, then it is equal to the largest subset of real numbers allowed by the rule.
Description of a function
-Step 1: we give a set which will be the domain of the function (H)
-Step 2: we describe the set which should contain the assigned elements (K) The notation for the sets of assignment is H→K, pronounced H arrow K
-Step 3: we give the assigment (the rule of ordering)
Variables, values
-The elements of the domain are called variables while the elements of the range are called values.
-We can substitute the variable of the rule by any element of the domain and determine the corresponding function value.
Giving the rule of a function
-There are several ways to describe the rule of a function. It can be done -with a formula
-in words
-with tablets
-with graphs
-with diagrams
Function's equality
-Def.: functions f: H1→ K1 x→ f(x) and g: H2→ K2 x→g(x) are said to be equal of and only if they have the same domain: H1=H2 and for any x element of set H we have f(x)=g(x)