The sketch shows the graphs of the functions f and g where y=f(x) = cx-p+q and g is a quadratic function such that the point (-1,3) lies on the graph of y = g(x). The salient point of the graph of y = f(x) is the point S (4,8). The line segment AB is parallel to the y-axis. Both the graphs of f and g pass through the origin O. (4.1) Determine the values of c, p and q and thus write down the equation of f. (4) (4.2) (2) If one of the X-intercepts of the graph of f is 0, use symmetry to determine the other X-intercept. Give a reason for your answer. 21 (4.3) Find the equation of g. (5) (4.4) Calculate the maximum length of AB if AB lies between O and S. (5) (4.5) (a) Restrict the domain of g so that the function g, defined by (2) gr (x) = g(x) all x € Dgr is a one-to-one function. Write down the set Dg₁. -1 (b) Find the equation of the inverse function gr¹, as well as the set D¹. (5) (4.6) (3) Use the graphs of f and g (not the algebraic expressions for f(x) and g(x)) to solve the inequality f(x) g(x) > 0 y = g(x)