Types of Functions1. Injective (OnetoOne) Functions: A function in which one element of Domain Set is connected to one element of CoDomain Set. 2. Surjective (Onto) Functions: A function in which every element of CoDomain Set has one preimage. Example: Consider, A = {1, 2, 3, 4}, B = {a, b, c} and f = {(1, b), (2, a), (3, c), (4, c)}. It is a Surjective Function, as every element of B is the image of some A Note: In an Onto Function, Range is equal to CoDomain.3. Bijective (OnetoOne Onto) Functions: A function which is both injective (one to  one) and surjective (onto) is called bijective (OnetoOne Onto) Function. Example: The f is a onetoone function and also it is onto. So it is a bijective function. 4. Into Functions: A function in which there must be an element of codomain Y does not have a preimage in domain X. Example: Therefore, it is an into function 5. OneOne Into Functions: Let f: X → Y. The function f is called oneone into function if different elements of X have different unique images of Y. Example: The function f is a oneone into function 6. ManyOne Functions: Let f: X → Y. The function f is said to be manyone functions if there exist two or more than two different elements in X having the same image in Y. Example: The function f is a manyone function 7. ManyOne Into Functions: Let f: X → Y. The function f is called the manyone function if and only if is both many one and into function. Example: As the function f is a manyone and into, so it is a manyone into function. 8. ManyOne Onto Functions: Let f: X → Y. The function f is called manyone onto function if and only if is both many one and onto. Example: The function f is a manyone (as the two elements have the same image in Y) and it is onto (as every element of Y is the image of some element X). So, it is manyone onto function
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