Let V be the space of continuous functions f : [-1.1] belonging to R. Decide if the following quantities are subspaces t
Posted: Tue Jul 05, 2022 9:57 am
Let V be the space ofcontinuous functions f : [-1.1] belongingto R. Decide if the followingquantities are subspaces to V.
(a) (b) (c) (d) ^= {ƒ©V: [ ' f(a)e ³dx=0}, B = {f V: f(x) ≤ [x], Vx € [−1, 1]}, C = {f V: f(-x) = f(x) Vr € [-1,1]} D={ƒ©V : [*² ƒ(a)²dx = [' f(2x)dx},
(a) (b) (c) (d) ^= {ƒ©V: [ ' f(a)e ³dx=0}, B = {f V: f(x) ≤ [x], Vx € [−1, 1]}, C = {f V: f(-x) = f(x) Vr € [-1,1]} D={ƒ©V : [*² ƒ(a)²dx = [' f(2x)dx},