The function p is defined on R by p(x)=∣x−1∣−2.
a. (i) Show that p attains only non-negative values and find the exact range of p.
b. (ii) Solve the inequality p(x)≤1. Express the solution set in interval notation.
c. (iii) Verify your answer to part (ii) by referring to the graph of y=p(x). (A sketch, not a precise plot, is sufficient.)