Nth repeated application of f
If
f
is a numerical function and
n
is a positive integer, then we can form the
n
th repeated application of
f
, which is defined to be the function whose value at
x
is
f(f(...(f(x))...))
. For example, if
f
is the function
x → x + 1
, then the
n
th repeated application of
f
is the function
x → x + n
. If
f
is the operation of squaring a number, then the
n
th repeated application of
f
is the function that raises its argument to the
2ⁿ
th power. Write a procedure that takes as inputs a procedure that computes
f
and a positive integer
n
and returns the procedure that computes the
n
th repeated application of
f
. Your procedure should be able to be used as follows:
((repeated square 2) 5)
625
Hint: You may find it convenient to use
compose
from exercise
1.42
.