What is absolute value of x plus 1 plus absolute value of x minus 1?

Answer 1

|x+1| + |x-1| = 2x, when x > 1 and -2x when x < -1, but between these two values, the value of the function is 2.

Here's how that works. If a function f(x) evaluates positive, then |f(x)| = f(x), but if f(x) evaluates negative then |f(x)| = -f(x).

So for x > 1, both functions are positive, so it's just x + 1 + x - 1 = 2x.

For x < -1, both functions are negative: -(x+1) -(x-1) = -x -1 -x + 1 = -2x

Between -1

x+1 - (x-1) = x + 1 - x + 1 = 2.