UPSKILL MATH PLUS

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The functions are of four types, namely:

1. One-to-one function

2. Many-to-one function

3. Onto function

4. Into function

Let us look at each of the functions in detail.
One-to-one function
Let $$f : A \rightarrow B$$ be a one-one function. Then, each distinct element in $$A$$ will have a distinct image in $$B$$.
Let us look at the representation given below for a better understanding.

In other words, if for all $$a_1$$, $$a_2$$ $$\in A$$, $$f(a_1) = f(a_2)$$ implies $$a_1 = a_2$$, $$f$$ is a one-to-one function.
A one-to-one function is otherwise called an injection.
Many-to-one function
Let $$f : A \rightarrow B$$ be a many-to-one function. Then, two or more elements in $$A$$ will have a distinct image in $$B$$.
Onto function
A function $$f : A \rightarrow B$$ is said to be onto function if the range of $$f$$ is equal to the co-domain of $$f$$.
That is, every co-domain will have a preimage.

An onto function is also called a surjection.

Into function
A function $$f : A \rightarrow B$$ is called an into a function if there exists at least one element in $$B$$ which is not the image of any element of $$A$$.