We know that f(f(x)) = x for all x. If x < 2, then f(x) = ax + b. Substituting into the first equation, we get

f(ax + b) = x

Since f(ax + b) = 8 - 3(ax + b) if ax + b >= 2, then we must have ax + b >= 2. This means that x >= -2/a.

If -2/a <= x < 2, then f(x) = ax + b. Substituting into the first equation, we get

(ax + b) + b = x

This simplifies to ax + 2b = x. Since ax + b >= 2, then x must equal 2. However, we know that f(2) = 8 - 3(2) = 2, so this case is not possible.

Therefore, the only possible value of x is x = -2/a. In this case, f(x) = f(-2/a) = 8 - 3(-2/a) = 10/a. Substituting into the first equation, we get

10/a + b = -2/a

This simplifies to a + b = -10. Therefore, a + b = −10