Racket Function with Two Arguments

Question

I'm trying to review my final exam in R5RS, but having trouble with a simple problem. My professor isn't really helpful and I don't know anybody in my class. Can you help me?

The function ratio takes in two parameters f (function) and x (a number). I had to use a let statement. The scheme function is supposed to produced an outcome for:

f(x)+f(x+1)/f(x)

This is what I have so far:

(define (ratio f x)
  (let ((f (+ x 1)))
    (/ (+ x (+ f 1))
       x)))

(ratio (lambda (x) (+ x 2)) 3)

I tried working with this for an hour, but still can't get the right answer.

Answer 1

Hint: let a = f(x) and let b = f(x + 1). What should the output be in terms of a and b?

In your solution, you bind f to the value of x + 1. So your solution is really calculating (x + (x + 2)) / x. You need to apply f to x, ie (f x).

Here is a start:

(define (ratio f x)
  (let ((a (f x)) (b (f (+ x 1))))
    ...))

Answer 2

Math               Scheme
f(x)               (f x)
x+1                (+ x 1)
f(x+1)             (f (+ x 1))
a/b                (/ a b)
a/f(x)             (/ a (f x))
f(x+1)/f(x)        (/ (f (+ x 1)) (f x))
c + f(x+1)/f(x)    ?
f(x) + f(x+1)/f(x) ?