1.Is it true that if f is continuous onto function on a closed interval then f(x) must also be a closed interval. How about the other way around. f is continuous and onto on a open bounded interval and f(x) is a closed interval 2. Relevant equations f:[0,1]-->(0,1) f:(0,1)-->[0,1] 3. The attempt at a solution There is a theorem that says that if f is continuous on a closed and bounded interval then set of f(x) is a closed and bounded interval.