The average annual costs for owning two different refrigerators for x years is given by the two functions: f(x) = 850 + 62x /x and g(x) = 1004 + 51x /xIn the long run, the cost of the refrigerator modeled by will be the cheapest, averaging $ per year.

Answer:In the long run cost of the refrigerator g(x) will be cheaper.Step-by-step explanation:The average annual cost for owning two different refrigerators for x years is given by two functionsf(x) = [tex]\frac{850+62x}{x}[/tex]      = [tex]\frac{850}{x}+62[/tex]and g(x) = [tex]\frac{1004+51x}{x}[/tex]              = [tex]\frac{1004}{x}+51[/tex]If we equate these functions f(x) and g(x), value of x (time in years) will be the time by which the cost of the refrigerators will be equal.At x = 1 yearf(1) = 850 + 62 = $912g(1) = 1004 + 51 = $1055So initially f(x) will be cheaper.For f(x) = g(x) [tex]\frac{850}{x}+62[/tex] = [tex]\frac{1004}{x}+51[/tex][tex]\frac{1004}{x}-\frac{850}{x}=1004-850[/tex][tex]\frac{154}{x}=11[/tex]x = [tex]\frac{154}{11}=14[/tex]Now f(15) = 56.67 + 62 = $118.67and g(x) = 66.93 + 51 = $117.93So g(x) will be cheaper than f(x) after 14 years. This tells below 14 years f(x) will be less g(x) but after 14 years cost g(x) will be cheaper than f(x).