The set RAF of rational functions of one real variable is the set of functions defined recursively as follows:

Question

I have no clue where to start on this problem... Here is the full problem (couldn't fit it on top). The set RAF of rational functions of one real variable is the set of functions defined recursively as follows: Base cases: ✏ The identity function, id(r)::== r for rER (the real numbers), is an RAF, ✏ any constant function on R is an RAF. Constructor cases: If f, g are RAF’s, then so is f ~ g, where ~ is one of the operations 1. addition 2. multiplication or 3. division. Prove by structural induction that RAF is closed under composition. That is, using the induction hypothesis, P(h)::== For all g E RAF, h o g E RAF prove that P(h) holds for all h E RAF.