Define g:R→R by g(x)=∣x∣+∣x−2∣.
a. (i) Write g(x) in explicit piecewise form, indicating clearly the interval attached to each expression.
b. (ii) Find the minimum value of g and the point(s) at which it occurs.
c. (iii) Solve the inequality g(x)≤3, giving the solution set in interval notation.