The function f(x) = -|x - b| intersects g(x) = 2(x - 4)2 at exactly one point. The value of b is:

To find the value of b, we need to set the two functions equal to each other and solve for x, then substitute x into one of the functions to find b.

Step 1: Set the functions equal to each other:

-|x - b| = 2(x - 4)^2

Step 2: Solve for x:

Because the absolute value function splits into two cases, we have:

Case 1: -(x - b) = 2(x - 4)^2 Case 2: x - b = 2(x - 4)^2

Solving these equations will give us the x-values where the functions intersect.

Step 3: Substitute x into one of the functions to find b:

Substitute the x-values from step 2 into the function f(x) = -|x - b| to find the corresponding b-values.

However, the problem states that the functions intersect at exactly one point. This means that the x-values from step 2 must be equal, and therefore the b-values must also be equal.

If the b-values are not equal, then there is no value of b for which the functions intersect at exactly one point.

If the b-values are equal, then that is the value of b for which the functions intersect at exactly one point.

Note: The above steps provide a general approach to solving the problem. However, without specific solutions for the x-values in step 2, we cannot provide a specific value for b.