Question

What is the importance of inverse functions?

Answer 1

Inverse functions are used in all sorts of contexts...

Explanation:

Here are a few application examples, but really inverse functions are used in most places you use functions...

When you encrypt a message, you probably expect someone to decrypt it later. Encryption is an example of a function, decryption being the corresponding inverse function.

If you are faced with a cubic equation of the form `ax^3+bx^2+cx+d = 0` to solve, the first step is typically to perform a Tschirnhaus transformation, substituting `t = x+b/(3a)` to derive a cubic equation of the form: `t^3+pt+q = 0`. Once you find the roots of this simpler cubic, you then need to map them to obtain the roots of the original cubic, using the mapping `x = t-b/(3a)`. This is an inverse function.

If you know how to permute three edges on the same face of a Rubik cube, but are faced with three edges in other positions to permute, then you may make a couple of moves to get the three edges on the same face, permute them in the way you know, then reverse the first couple of moves you made. This is using an inverse function.