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