How to check to see if a function in R is a constant function?

Question

An R function is passed to me, which is defined on some interval of the Real Line and returns a numeric value. Is there a way to check to see if the function is constant?

Example functions:

f1<-function(x) {11}
f2<-function(x) {x+2}
f3<-function(x) {1+1}
f4<-function(x) {return(3)}

I am looking for a test that will say that f1,f3,f4 are constant functions but f2 isn't. Any Ideas?

Edit:

Frank's and Gregor's (edit: and Michael Lawrence's second solution)solutions below all work for all the 4 test cases given above (Marat's and Michael's don't work on all 4 cases). So there is already solutions. But extra bonus points if you can find a solution which also gives the right answer for the following 3 test functions:

f5 <- function(x) ifelse(x == 5.46512616432116, 0, 1)
f6 <- function(x) ifelse(x == 5.46512616432116, 0, 0)
f7 <- function(x) {x - x}

Answer 1

Try functionBody:

> is.numeric(functionBody(f1)[[2]])
[1] TRUE

> is.numeric(functionBody(f2)[[2]])
[1] FALSE

Answer 2

These code-based tests are clever and fun to see, but so far I think the "try a bunch of numbers" approach may be a more powerful test, depending on the type of functions you might get and whether you care more about Type I or Type II errors in your identification.

In your question, you say

which is defined on some interval of the Real Line

So let's assume we know the domain of interest. Sample some number of points on that domain, and test your function.

n = 1e5
test = runif(n, min = 0, max = 5)
results = f(test) # sapply(test, f) if f isn't vectorized

# test for constancy
all(results == results[1]) # or all(diff(results) == 0) or however else

Any function that is truly a constant function will pass this test just fine, no matter how pathological---this will not be true for any of the other methods suggested so far. However, it is quite easy to fool the test with the example I left in the comments (or anything of this sort)

f3 = function(x) ifelse(x == 5.46512616432116, 0, 1)