If f(x) = |x - 1| + |x - 2|, what is the simplified form of f(x) when 1 < x < 2?

Model Answer & Options

Source: Extra Practice

1

2x - 3

3 - 2x

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.

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