To find the inverse of a one-to-one function, do the following:

Since 0,0),(1,1) is injective (one to one) and surjective, then it is bijective function.

Since 0,1),(1,0) is injective (one to one) and surjective, then it is bijective function.

Since 0,0),(-6,6) is injective (one to one) and surjective, then it is bijective function.

Since -5,9),(3,0) is injective (one to one) and surjective, then it is bijective function.

Given a bijective function f between two topological spaces, the inverse function f−1 need not be continuous.

Two sets are said to have the same cardinality when there is a bijection (1-1 correspondence) between them.

As a word of caution, "a one-to-one function" is one that is injective, while a "one-to-one correspondence" refers to a bijective function.

Further, the hash value calculation device calculates a hash value via a bijective function (g) by inputting the calculated values y1[L] and y2[L] as input values.

They are called similar if there exists a positive constant k > 0 and a bijective function f, called similarity such that f : M1 → M2 and d2(f(x), f(y)) = k d1(x, y) for all x, y in M1.

They are called similar (of the second type) if there exists a bijective function f, called similarity such that f : M1 → M2 and d2(f(x), f(y)) = d2(f(u), f(v)) if and only if d1(x, y) = d1(u, v) for all x, y,u, v in M1.

Showing a function is bijective and finding its inverse

To find the inverse of a one-to-one function, do the following:

A function is bijective if it is injective and surjective.

Finally, if a function is injective and surjective, then it is bijective.