If \(x\) is a real number such that \(\max(\min(x, 2 - x), x - 4, 2x - 8) = \pi - 3\), then the number of possible values of \(x\) is

f(x) = x for x <= 1; f = 2-x on [1,3]; f = x-4 on [3,4] (values -1 to 0); f = 2x-8 for x >= 4. Setting f = pi-3 (about 0.142): x = pi-3, x = 5-pi, x = (pi+5)/2; the [3,4] piece never reaches a positive value. Three values.