The Inverse of a Function
Denoted by , the inverse of a function is a function that undoes the original transformation.
Let's say that we had a function that doubled every number you give to it:Of course, this function is injective. We can undo it, or invert it, by dividing the image:
So, how do we generally find the inverse of a function?
Lets say you have a function of form not f(x), but y in terms of x, for example: We have a function that gives us y in terms of x.
To find the inverse of that function, all we have to do is solve this same equation to find x in terms of y:
Indeed, we have found the inverse of f(x) = 2x+4 in terms of y:As you can see, the inverse of a function is a map that brings the image of the original function back to its domain, while the original function brings its domain to the image.