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  2

Step-by-step explanation:

The average rate of change is the slope of the line connecting the two points of interest. Here, that line has a rise of 2 units for each run of 1 unit, so its slope is ...

  rise/run = 2/1 = 2

The average rate of change of g on [-4, 2] is 2.

x =±sqrt(1/3)

step-by-step explanation:

x+4/6x=1/x

multiply each side by 6x to get rid of the fractions

6x*(x+4/6x)=1/x*6x

distribute

6x^2 +4 = 6

subtract 4 from each side

6x^2 +4-4 = 6-4

6x^2 =2

divide by 6

6x^2/6 = 2/6

x^2 = 1/3

take the square root of each side

sqrt(x^2) = ±sqrt(1/3)

x =±sqrt(1/3)