inverse function (original) (raw)

Properties

1. 1. When an inverse function exists, it is unique.
2. 1. The inverse function and the inverse image of a set coincide in the following sense. Suppose f-1⁢(A) is the inverse image of a set A⊂Yunder a function f:X→Y. If f is a bijection, then f-1⁢(y)=f-1⁢({y}).
3. 1. The inverse function of a function f:X→Y exists if and only if f is a bijection, that is, f is an injection and a surjection.

Remarks

When f is a linear mapping (for instance, a matrix), the term non-singular is also used as a synonym for invertible.