Reply to comment

Exercise 1.43

Printer-friendly versionPrinter-friendly version

If f is a numerical function and n is a positive integer, then we can form the nth 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 xx + 1, then the nth repeated application of f is the function xx + n. If f is the operation of squaring a number, then the nth repeated application of f is the function that raises its argument to the 2nth 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 nth 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.

Corresponding Section: 

Reply

  • Web page addresses and e-mail addresses turn into links automatically.
  • Allowed HTML tags: <a> <em> <strong> <cite> <code> <pre> <hr> <ul> <ol> <li> <dl> <dt> <dd> <img>
  • Lines and paragraphs break automatically.
  • Adds typographic refinements.

More information about formatting options