Let f : R → R with intermediate value property and increasing over R \...
Let with intermediate value property and increasing over \. Then is continous on . How to try?
Answer & Explanation
Let be real. Take an irrational number such that . Clealry , for if not, then
by our hypotesis, which is absurd. By the same argument if is irrational and . Hence is increasing on the whole line. Can you take it from here?