It is a formula that is the reverse of another one.
I.e if you put x = 1 into a formula and get y = 5, with the inverse formula you would put x =5 and get y = 1.
To work out an inverse I will give an example:
Y = 2X + 7
there are 2 ways to do it, but my favourite is to replace ys with xs and vice versa so:
X = 2Y + 7
rearrange to get it as Y =...
2Y = X - 7
Y = (X-7)/2
Now put in a number like x = 5 into the top equation and you get y = 17 then putting x = 17 into the bottom equation you get 5, which means it is correct, the inverse.
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For any number a (not zero) there exists a number 1/a such that a x (1/a) = 1
Put simply, the inverse of y=x^5+x^4+x is x=y^5+y^4+y. Unfortunately, this is a quintic function and there is no quintic formula.
The formula for the derivative of an inverse (finv)' = 1/(f' o (finv)) allows you get a formula for the derivative of the inverse of any function that you already know the derivative of. For example: What is the derivative of sqrt(x)? You could figure this out using the definition of the derivative, but it is complicated. You already know that the derivative of x2 is 2x. So let f = x2; finv = sqrt(x), f' = 2x. This gives: (sqrt(x))' = 1/(2 sqrt(x)). Now you have derived a "square root rule" with almost no work.
* *It is the reverse of the actionEx.Addition is the inverse of subtrationmultiplication is the inverse of division
Addition is the inverse operation of subtraction and multiplication is the inverse operation of division. The word inverse means "opposite".