Consider the two functions: f(x) = 1 -x and g(x) = We can compose them in two ways: f(g(x)) and g(f (x)) We can also compose each function with itself: f(f (x)) and g(g(x)) We can go further and compose each of these new functions with themselves, and also with the old ones, in a number of ways. For example, f (9 (f ( x ) ) ) g (9(f ( x ) ) ) f(f ( f ( x ) ) ) can all be calculated from the original two functions. Keep composing these functions with new ones as they are generated and figure out simplified formulae for them in terms of the variable x. You might think that more and more new functions will be generated. Surprisingly, only a finite number of new ones get generated by composition, even though there may be many different ways of composing f and g to get the same function. Remember that two very different looking formulae may represent the same function. How many different functions are there, including f and g themselves? List them, and show at least one way in which each function is composed from f and g. For what real numbers are all these functions simultaneously defined