Prove for Continuity of Minimum and Maximum Functions
a) , show that f_1(x) is continuous.
b) show that f_4(x) is continuous.
where and are both continuous.
a) I was thinking of splitting up into 2 where I assume firstly that is the minimum secondly where . Thus if the minimum is then thus for it to be continuous on any point c there exist a s.t. .
now if I is the minimum then just replace by f_3(x).
b) I would think this would be the same type of procedure as in a), where we have to split them up and show that individually they are continuous.
Would this be the correct way of doing it?