Suppose that f is a continuous function on the closed interval [a, b) and that a

Suppose that f is a continuous function on the clused interval la, bl and that a f (x) b for all e [a, bl. Prove that there rnll.st exist a point :r = e la,bl such that f (:r) = :r. The point is called a fixed point of f Hints: If f(a) = a or f (b) b then them nothing mom to prove, so look at the case when f (a) / a and f(b) / b In mathematics when you nerd to show that two things am equal it is often much easier to show that their differencx is zero. In other words, try letting g(x) = f (x)