need help with problem 5

4. Show that (f: new) of s (Alumnae) (freeman) for all continuous functions g : [i], 1] 1~ 1R. Hint: there are tons of ways to do this problem. In my opinion the best approach uses the observation that [U 1w) eye)? as: a u for all constants e and then picks a good choice of c. 5. Give an example of f(fl') and mix) that shows the inequality in the previous problem may be strict