Question

Let A = {x ∈ R: -1 ≤  x ≤1} = B. Show that f :A → B given by f(x) = x l x l is a bijection.

Answer 1

We have,

Since any line parallel to x-axis, will cut the graph at only one point, so f is one-one. Also any line parallel to y-axis will cut the graph, so f is onto. 

Thus, it is evident from the graph of f(x) that f is one-one and onto.