It is known that the zero point of function f (x) = | X-1 | ^ 3-2 ^ | X-1 | (the intersection of function and X axis) has four zeros X1 x2 x2 x3x4 Find f (x1 + x2 + X3 + x4) = how many, do not copy the answer, I want to know how to find the function about where symmetry

It is known that the zero point of function f (x) = | X-1 | ^ 3-2 ^ | X-1 | (the intersection of function and X axis) has four zeros X1 x2 x2 x3x4 Find f (x1 + x2 + X3 + x4) = how many, do not copy the answer, I want to know how to find the function about where symmetry

Let t = | X-1 |, then f (x) = T ^ 3-2 ^ t
Since t is symmetric with respect to x, it is obvious that the function f (x) is also symmetric with respect to the line x = 1
If P is zero, i.e. f (P) = 0, then q = 2-P is also zero
Because f (1) = - 1, x = 1 is not zero
So the zeros of F (x) appear in pairs, and the sum of each pair is p + q = 2
So f (x1 + x2 + X3 + x4) = f (2 + 2) = f (4) = 3 ^ 3-2 ^ 3 = 27-8 = 19