SOLUTION: Let T : C[0,1] → R be given by T(f) = f(0) + 3f′(0) + 2f′(1). Is T one-to-one?

Algebra ->  College  -> Linear Algebra -> SOLUTION: Let T : C[0,1] → R be given by T(f) = f(0) + 3f′(0) + 2f′(1). Is T one-to-one?      Log On


   

Question 1170166: Let T : C[0,1] → R be given by
T(f) = f(0) + 3f′(0) + 2f′(1).
Is T one-to-one?
Answer by ikleyn(52776) About Me  (Show Source):
You can put this solution on YOUR website!
.

This problem is posed incorrectly. 

    The space C[0,1] is the space of continuous functions on interval [0,1] (standard designation).


    Not every continuous function has a derivative and is differentiable.


    Meanwhile, the definition of the map T(f) assumes existing of the derivatives f'(0) and f'(1).

It is a  RUDE  MISTAKE,  unpardonable for a university  Calculus student/professor.


Learn the basics of your science.