Prove for Continuity of Minimum and Maximum Functions

Let

**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?