Sketch the graph of an invertible function f(x) that intersects its inverse in exactly three points.
The Attempt at a Solution
I dont know where to start... Can I pick any function to start with?
Yes, that's right. So in order to satisfy "intersects its inverse in exactly three points" there must be exactly three values of x such that f(x)= x. That is the same as saying f(x)- x= 0 for exactly three values of x. However the problem is making sure f is invertible then. You need to go from each such x to the next without having negative slope.This is an interesting problem because from what I remember functions and their inverses only intersect on the identity function y=x