Provide a recursive definition of the function f (n) = (n+1) !.

See definition below

Step-by-step explanation:

Since we have to give a recursive definition, we must give a initial value f (0). Additionally, the value of f (n) must depend on the value of f (n-1) for all n≥1.

The required value of f (0) is (0+1) !=1!=1.

Now, the factorial itself is a recursive function, because (n+1) ! = (n+1) n!. In terms of f, this means that f (n) = (n+1) f (n-1) for all n≥1.

Then, our definition is: f:N→N is defined by

f (0) = 1. For n≥1, f (n) = (n+1) f (n-1).