Suppose that f(x) and g(x) are functions on {R} such that the range of f is [-5,3], and the range of g is [-2,1]. The range of f(x).g(x) is [a,b]. What is the largest possible value of b?
The smallest value of f is -5, that of g is -2. The product of these is +10, so 10 is the maximum value of b. Here is one of an infinite number of possible examples:
