Solving for the inverse of a function in R

inverse, r

Solution

What kind of inverse are you finding? If you're looking for a symbolic inverse (e.g., a function y that is identically equal to sqrt(x)) you're going to have to use a symbolic system. Look at ryacas for an R library to connect with a computer algebra system that can likely compute inverses, Yacas.

Now, if you need only to compute point-wise inverses, you can define your function in terms of uniroot as you've written:

> inverse = function (f, lower = -100, upper = 100) {
   function (y) uniroot((function (x) f(x) - y), lower = lower, upper = upper)[1]
}

> square_inverse = inverse(function (x) x^2, 0.1, 100)

> square_inverse(4)
[1] 1.999976

For a given `y` and `f(x)`, this will compute `x` such that `f(x) = y`, also known as the inverse.

Problem

Is there any way for `R` to solve for the inverse of a given single variable function? The motivation is for me to later tell `R` to use a vector of values as inputs of the inverse function so that it can spit out the inverse function values. For instance, I have the function `y(x) = x^2`, the inverse is `y = sqrt(x)`. Is there a way `R` can solve for the inverse function? I looked up `uniroot()`, but I am not solving for the zero of a function. Any suggestions would be helpful. Thanks!

Original source