Define p:[−4,4]→R by p(x)=∣x∣+1.
a. (i) Show that p is not invertible on the given domain.
b. (ii) Restrict the domain suitably so that the resulting function becomes invertible, and obtain the inverse in explicit piecewise form.
c. (iii) Sketch on the same axes the graphs of p and p−1 obtained in part (ii), indicating clearly the line y=x and the points of intersection.