get x-value given y-value: general root finding for linear / non-linear interpolation function

Question

I am interested in a general root finding problem for an interpolation function.

Suppose I have the following (x, y) data:

set.seed(0)
x &         


        

Answer 1

Given data points and spline function as above, simply apply findzeros() from the pracma package.

library(pracma)
xs <- findzeros(function(x) f3(x) - 2.85,min(x), max(x))

xs  # [1] 3.924513 6.435812 9.207169 9.886618
points(xs, f3(xs))