The function f(x) = -|x - b| intersects g(x) = 2(x - 4)2 at exactly one point. The value of b is:A.Any real number.B.-4C.4D.-5E.5

To solve this problem, we need to find the value of 'b' for which the functions f(x) = -|x - b| and g(x) = 2(x - 4)² intersect at exactly one point.

Step 1: Set the two functions equal to each other to find the x-values where they intersect.

-|x - b| = 2(x - 4)²

Step 2: Solve for x in terms of b.

This equation is a bit tricky because of the absolute value. We know that the absolute value of a number is always positive, so the left side of the equation is always negative while the right side is always positive. Therefore, the only way for these two sides to be equal is if they are both equal to zero.

So, we have two equations:

x - b = 0 and 2(x - 4)² = 0

Solving these gives x = b and x = 4.

Step 3: Since the functions intersect at exactly one point, x = b = 4.

So, the correct answer is C. 4.