The average value of the function f(x) = 2x - 2 over the interval [-3, 5] is given by the formula:
f(c) = (1/(b-a)) * ∫[a to b] f(x) dx
Where a = -3, b = 5, and f(x) = 2x - 2. Plugging these values into the formula gives:
f(c) = (1/(5-(-3))) * ∫[-3 to 5] (2x - 2) dx
Solving the integral gives:
f(c) = (1/8) * [x^2 - 2x] from -3 to 5
f(c) = (1/8) * [(5^2 - 2*5) - ((-3)^2 - 2*(-3))]
f(c) = (1/8) * [25 - 10 - 9 + 6]
f(c) = (1/8) * 12
f(c) = 1.5
Therefore, the average value of the function f(x) = 2x - 2 over the interval [-3, 5] is 1.5.