Final answer:
In functional programming, 'let f = fun x -> e' and 'let f x = e' are two syntaxes for defining a function 'f', with both resulting in the same behavior.
Step-by-step explanation:
In programming, specifically in functional languages like OCaml, the expressions let f = fun x -> e and let f x = e are both ways to define a function named f. While both expressions establish a binding to a function f, they use slightly different syntax. The expression let f = fun x -> e uses an explicit fun keyword to define a function that takes an argument x and evaluates to e. On the other hand, let f x = e uses a more shorthand syntax where the argument x is placed directly after the function name, and the expression e defines the body of the function. Functionally, both definitions result in the same behavior, creating a function that takes one argument and evaluates the expression e with respect to that argument.