The function tan(x)=x has 1. Unique fixed point 2. No fixed point 3. Infinite many fixed points 4. More than one but finitely many fixed points.
My attempt: I have solved this problem by graphical approach. The intersecting points of the function y=tan(x) and the line y=x are fixed points that I obtained which are infinite. But my problem is that how to solve it without graphical approach and how to discard options. Is there any general approach to tackle this type of problems?