Conditional application

Write a function apply_if that takes as input a predicate p, a function f, and a value x. The output is:

f x, if p x is true;
x, otherwise.

The function must have the following type:

apply_if : ('a -> bool) -> ('a -> 'a) -> 'a -> 'a

Here are some unit tests:

let is_even = fun x -> x mod 2 = 0;;
let is_odd = fun x -> not (is_even x);;
let double x = x * 2;;

assert(apply_if is_even double 4 = 8);;
assert(apply_if is_even double 5 = 5);;
assert(apply_if is_odd double 4 = 4);;
assert(apply_if is_odd double 5 = 10);;