Functions in math have paramount importance and let us study different types of functions. We have four functions based on the mapping of elements from set A to set B.
- f: A → B is said to be one-to-one or injective, if the images of distinct elements of A under f are distinct, i.e, for every a, b in A, f(a) = f(b), ⇒ a = b. Otherwise, it is many-to-one.
- f: A → B is said to be onto, if every element of B is the image of some element of A under f, i.e, for every b ϵ B, there exists an element a in A such that f(a) = b. A function is onto if and only if the range of the function = B.
- f: A → B is said to be one-to-one and onto or bijective, if f is both one-one and onto.
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