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

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(52777) (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.

RELATED QUESTIONS
Let the function f be defined by f(x)=x(x)-7x+10 and f(t+1)=0 , what is one possible... (answered by stanbon)

Let the function f be defined by f(x)=x^2-7x+10 and f(t+1)=0, what is one possible value... (answered by bloggauta)

Use the characteristics of f(t) = sin t to find the value of sin t when t = �12π. (answered by Fombitz)

Define T : P2(R) → M2(R) by T(f) = [f(1) − f(2) 0 ] [ 0 (answered by ikleyn)

A. Let g(t) be the solution of the initial value problem 4t(dy/dt)+y=0, t>0, with... (answered by robertb)

Let T be the life length of a mechanical system. Suppose that the cumulative distribution (answered by ikleyn)

{{{ Let f (x) = 1/x^2 (sqrt(25 + x^2)) }}} {{{ and g(t) = 5 tan(t) for 0 < t < pi/2 }}} (answered by jim_thompson5910)

1. Whenever we encounter a new proposition, it is a good idea to explore the proposition (answered by richard1234)

please help im going insane!!! {{{f(t)=1+tcos(pi*t),0<=t<=1}}} and... (answered by jim_thompson5910)