Inverses

Another topic which can be represented graphically and explained using real life examples.

In terms of functions, let's consider the functions f(x) and g(x), g(x) is the inverse of f(x) if for all values of x we find that
f(g(x)) = x or g(f(x)) = x.
We can also say that f takes x to f(x) and then g takes f(x) back to x. (Think of reversing a process.)

Inverses exist in a lot of fields of mathematics. We can have invertible matrices, for example. If A is a matrix, then B is the inverse only if
AB = I
where we refer to I as the identity matrix (a matrix with 1's along it's diagonal and all other entries 0).

We can also think of it in terms of spaces, where the function f takes us from space A to space B, and the inverse of f takes us back from B to A.

An easy example is the inverse of a number. For example the multiplicative inverse of 3 is just ⅓ since the product equals 1.

We can also have the additive inverse of a number.

Lets consider a few possibilities of inverses in our daily lives.
Suppose we could take the inverse of time, then that would mean that we would be able to go back in time, and in principle also go to the future.
An inverse can be undoing an action, for instance tying your shoe is f(x) and untying your shoe is the inverse g(x).

Inverse(The beginning) =  The end.

(Images taken from: http://regentsprep.org)