Source: Extra Practice
If f(x) = |x - 1| + |x - 2|, what is the simplified form of f(x) when 1 < x < 2?
Options
Option A is correct
1
Option B
2x - 3
Option C
3 - 2x
Option D
0
Explanation
In the interval 1 < x 0, so |x - 1| = x - 1. (2) x - 2 < 0, so |x - 2| = -(x - 2) = 2 - x. Therefore, f(x) = (x - 1) + (2 - x) = 1. This shows that the function is constant between its roots. Option B is for x ≥ 2. Option C is for x ≤ 1. Option D is mathematically incorrect calculation.