Let
be a continuous function from the interval [ a , b ] {\displaystyle {}[a,b]} into itself. Prove that f {\displaystyle {}f} has a fixed point.
![{\displaystyle f\colon [a,b]\longrightarrow [a,b]}](https://wikimedia.org/api/rest_v1/media/math/render/svg/053f08d10648e72e31514c3bdd65f71e3ac40bb2)
![{\displaystyle {}[a,b]}](https://wikimedia.org/api/rest_v1/media/math/render/svg/8e5a6e660b5cdc1a9c76f6e6b0d486328c3f6937)
