Answer:
Step-by-step explanation:
The average rate of change is given by [g(x_2) - g(x_1)]/(x_2 - x_1). Here, we have x_1 = -2, x_2 = -2 + h, and g(x) = 4/x, so we get:
Average rate of change
= [g(x_2) - g(x_1)]/(x_2 - x_1)
= [4/(-2 + h) - 4/(-2)]/[(-2 + h) - (-2)]
= [4/(-2 + h) + 4/2]/(-2 + h + 2)
= [4/(-2 + h) + 2]/h
To simplfiy this, we combine fractions in the numerator:
[4/(-2 + h) + 2]/h
= [4/(-2 + h) + 2(-2 + h)/(-2 + h)]/h
= {[4 + 2(-2 + h)]/(-2 + h)]}/h
= [(4 - 4 + 2h)/(-2 + h)]/h
= [2h/(-2 + h)]/h
= 2/(-2 + h)
So the average rate of change of g(x) = 4/x between x = -2 and x = -2 + h is 2/(-2 + h).
I hope this helps!
