Question

What are inverses?

Answer 1

inverse function? inverse matrix?

Answer 2

an inverse function is a function that in some sense undoes another function: if ƒ is a function from a set A to a set B, then the inverse of ƒ is a function from B to A, with the property that a round trip from A to B to A (via a composition of ƒ and its inverse) returns each element of A to itself. Thus, if an input x into the function ƒ produces an output y, then inputting y into the inverse function produces the output x, and vice versa.

A function ƒ that has an inverse is called invertible; the inverse function is then uniquely determined by ƒ and is denoted by ƒ−1 (read f inverse, not to be confused with exponentiation).

A relation can be determined to have an inverse if it is a one-to-one function.