19.3.15 Linear Operators

Condition: Prove that the following functionations in space \ (C [-1,1] \) are linear continuous and find their norms. a) \ (f (x) = \ frac {1} {3} (x (-1)+x (1)), b) \ (f (x) = 2 (x (1) -x (0)), c) \ (f (x) = \ int_ {0}^{1} x (t) d t \), g) \ ( f (x) = \ int _ {-1}^{1} x (t) d t-x (0) \), e) \ (f (x) = \ int _ {-1}^{1} t x (t) d t \)