AoPS

MATHEMATICS · Multi-part · AoPS · Mathematics · Special Functions · Special Functions

Problem

Define

g: \mathbb{R} \to \mathbb{R}

g(x)=|x|+|x-2|

. (i) Write

g(x)

in explicit piecewise form, indicating clearly the interval attached to each expression. (ii) Find the minimum value of

g

and the point(s) at which it occurs. (iii) Solve the inequality

g(x)\le3

, giving the solution set in interval notation.