Dealing with absolutes

Algebra Level 2

Let $f(x) = |x| - |x-1|$

Let $A$ be the maximum value of $f(x)$ and $B$ be the minimum value of $f(x)$ .

Find $A - B$ .

Notation : $| \cdot |$ denotes the absolute value function .

4 0 3 1 2

1 solution

Denton Young
Jul 20, 2016

The maximum value of f(x) is 1, at any value of x greater than or equal to 1.

The minimum value of f(x) is -1, at any value of x less than or equal to 0

1 - (-1) = 2