Could someone please check this proof and let me know if it's correct

use state all definitions and theorems that you will need: [ 20 pts ) 1 Let f be a function defined on an interval I . We say that f is strictly increasing if a, f(x2) Prove the following. 2. If f is strictly increasing and if f(1) is an interval, then f is continuous. Furthermore, f -1 is a strictly increasing continuous function on f(1) . Let I = [a, b] and CE (a, b). = f (a) s f (c) s f (b) and a s c b since f is strictly increasing I f ( c ) - f (b), set $2 = 6 so that $2 E I IF f ( c ) + Es f ( b ) , 32 2 > c = f (12) = f (c ) + ; In either case, f (22 ) = f (c ) + ; By the Intermediate Value Property mentioned in the Intermediate Value Theorem, f (c) s f (2)