Consider the functions f(x) number. a) Describe the end behaviour of f(x) and, hence, find the horizontal asymptote. = x3 and g(x) = -3x+a, where a is a non-zero real b) Determine the zeros and the y-intercept of g(x), if they exist. c) Find the compositions (gof)(x) and (fog)(x). d) Determine the unique value of a such that f and g are inverse functions of each other. e) For that a-value, state the domain and the range of f and g, and sketch their graphs on the same axes.