19.3.15 Linear operators

Condition: Prove that the following functionals in the 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) \( f(x)=\int_{0}^{1} x(t) d t \), d) \( f(x)=\int_{-1}^{1} x(t) d t-x(0) \), d) \( f(x)=\int_{-1}^{1} t x(t) d t \)