In general, you can't find the range of numbers f(x) * g(x) takes just knowing the ranges for f(x) and g(x). For example, f(x) may have a minimum or a maximum where g(x) has a maximum. In this case, however, this is possible because both |x - 1| and |x - 3| get their maximum in the same point x = 5. (Note that x is strictly less than 5.) I would still recommend drawing the graph of |2x^2 - 8x + 6| over the allowed values of x and finding the image from there.