FunctionsIt is a mapping in which every element of set A is uniquely associated at the element with set B. The set of A is called Domain of a function and set of B is called Co domain. Domain, CoDomain, and Range of a Function:Domain of a Function: Let f be a function from P to Q. The set P is called the domain of the function f. CoDomain of a Function: Let f be a function from P to Q. The set Q is called Codomain of the function f. Range of a Function: The range of a function is the set of picture of its domain. In other words, we can say it is a subset of its codomain. It is denoted as f (domain). Example: Find the Domain, CoDomain, and Range of function. Solution: Domain of function: {1, 2, 3, 4} Range of function: {a, b, c, d} CoDomain of function: {a, b, c, d, e} Functions as a SetIf P and Q are two nonempty sets, then a function f from P to Q is a subset of P x Q, with two important restrictions
Note1: There may be some elements of the Q which are not related to any element of set P.2. Every element of P must be related with at least one element of Q.Example1: If a set A has n elements, how many functions are there from A to A? Solution: If a set A has n elements, then there are n^{n} functions from A to A. Representation of a FunctionThe two sets P and Q are represented by two circles. The function f: P → Q is represented by a collection of arrows joining the points which represent the elements of P and corresponds elements of Q Example1: Then f can be represented diagrammatically as follows Example2: Let X = {x, y, z, k} and Y = {1, 2, 3, 4}. Determine which of the following functions. Give reasons if it is not. Find range if it is a function.
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