what makes a function invertible? - Mathematics Stack Exchange
Aug 30, 2021 · And a function is invertible if and only if it is one-to-one and onto, i.e. the function is a bijection. This is not necessarily a definition of invertible, but it a useful and quick way of deciding if a …
Is a bijective function always invertible? - Mathematics Stack Exchange
Sep 3, 2017 · A function is invertible if and only if it is injective (one-to-one, or "passes the horizontal line test" in the parlance of precalculus classes). A bijective function is both injective and surjective, thus …
Is every injective function invertible? - Mathematics Stack Exchange
Sep 25, 2015 · A function is invertible if and only if it is bijective (i.e. both injective and surjective). Injectivity is a necessary condition for invertibility but not sufficient.
The difference between inverse function and a function that is invertible?
Apr 10, 2018 · So for a function to have a inverse, it must be bijective. But any function that is injective is invertible, as long as such inverse defined on a subset of the codomain of original one, i.e. the image …
Invertible function without onto - Mathematics Stack Exchange
Aug 9, 2017 · I have come across a situation in differential calculus where my mentor said that a function is invertible if it is one one because we consider range of function as domain of function's …
Does a function need to be either surjective, injective, or bijective ...
An invertible function shall be both injective and surjective, i.e Bijective! where every elemenet in the final set shall have one and only one anticident in the initial set so that the inverse function can exist!
"invertible function" is the same thing as "one to one correspondence ...
Apr 24, 2020 · “Invertible function” may be different from the other two depending on the context. For example, in topology, not every bijection is invertible (because not every continuous bijection has a …
elementary set theory - Invertibility of a function and left/right ...
Also note that $g$ is a right invertible function without a left inverse for the same reasons. You can, however (as you appear to say), make a left invertible function invertible by restricting the range.
Invertible function $f:\mathbb {N} \rightarrow (0,1)$ [duplicate]
Apr 2, 2025 · [1] I guess this depends on the definition of "invertable" and whether it means invertable from the functions image (everything mapped to can be uniquely mapped back-- then all invertable is …
Understanding the difference between pre-image and inverse
Jul 7, 2019 · For starters, they are two very different objects. The pre-image of a function is a subset of the domain and the inverse function is a function from the range back to the domain that satisfies …