1. The problem asks for the average value of the function $$f(x) = e^{x^2 - 2x}$$ on the interval $$[-1, 3]$$. 2. The formula for the average value of a function $$f(x)$$ on $$[a,b]$$ is: $$\text{Average value} = \frac{1}{b-a} \int_a^b f(x) \, dx$$ 3. Here, $$a = -1$$ and $$b = 3$$, so the average value is: $$\frac{1}{3 - (-1)} \int_{-1}^3 e^{x^2 - 2x} \, dx = \frac{1}{4} \int_{-1}^3 e^{x^2 - 2x} \, dx$$ 4. The integral $$\int e^{x^2 - 2x} \, dx$$ does not have an elementary antiderivative, so we use a graphing calculator or numerical integration to approximate: $$\int_{-1}^3 e^{x^2 - 2x} \, dx \approx 29.996$$ 5. Substitute this value back into the average value formula: $$\text{Average value} \approx \frac{1}{4} \times 29.996 = 7.499$$ 6. Rounded to three decimal places, the average value is: $$\boxed{7.499}$$