How can I do something like double a polynomial?

I have this:

b <- function(ftn){2*ftn}
b(function(x) x)

But I get Error in 2 * ftn : non-numeric argument to binary operator

Is there some sort of x <-2x replacement I can do?

Sorry I'm a complete beginner.

• r
• func

Yes, but you do it by returning an anonymous function that takes the x value, calls ftn and applies the transformation. e.g. for f(x) ↦ 2f(x):

> doublePoly <- function(ftn) { function(x) { 2 * ftn(x) } }
> f <- function(x) {x^2 + 1}
> g <- doublePoly(f)
> c(f(1), g(1))
[1] 2 4
> c(f(3), g(3))
[1] 10 20

One can use this technique to do arbitrary transformations, e.g. multiplying by 1+x:

mult.1plusx <- function(ftn) { function(x) { (1+x) * ftn(x) } }

Or adding exp(x) to the logarithm of the function:

exp.plus.log <- function(ftn) { function(x) { exp(x)  + log(ftn(x)) } }