Could someone please help me improve this proof

Let f be a function defined on an interval I . We say that f is strictly increasing if x1 f(x2) Prove the following. asian an strinthis darraacing 2. If f is strictly increasing and if f(I) is an interval, then f is continuous. Furthermore, f - is a strictly increasing continuous function on f(I) . Ler f be a function defined on an interval I. Prove That if of is strictly increasing and if f (I) is an interval, Then of is continuous. Furthermore, fal is a strictly increasing Continuous function on f(I). Ler I = [a,b]. Since f is strictly increasing Then for all Xnext, in I There is Andall K between F( x,) and f (x, +. ) , it is always possible To find a point CE (Xr, Xnyi) where f(c ) = K. Since all f(x,)