If f(x) = 1/x - 2, then the average rate of change between x = 4 and x = 8 is
(f (8) - f (4)) / (8 - 4) = ((1/8 - 2) - (1/4 - 2)) / 4 = -1/16
If you meant f(x) = 1/(x - 2), then it would be
(f (8) - f (4)) / (8 - 4) = (1/(8 - 2) - 1/(4 - 2)) / 4 = (1/6 - 1/2) / 4 = -1/12
Make sure to check which one is the correct function!
