Remember that if f and g are inverses of one another, then
f(g(x)) = g(f(x)) = x
1/2. Take a = 0 and b = 1 (or any non-zero number) so that
f(x) = x + 0/1 ⇒ f(x) = x
If g is to be an inverse of f, we need
g(f(x)) = g(x) = x
so that c = 1 and d = 0.
3. With f(x) = x + a/b and g(x) = cx - d, we have
g(f(x)) = g(x + a/b) = c (x + a/b) - d = cx + ac/b - d
and of course, with a,b,c,d as before, we get g(f(x)) = x.
4. This would be a very uninteresting graph for the example I've cooked up here, just containing the line y = x...
