State whether the following statements are True or False? Justify your answers with the help of a short proof or a counter example: (10)
 a) The function f, defined by  is an odd function.
 b) 

 c) The function f, defined by  is differentiable in [0,1].
 d)  has no points of inflection.
 e)  is increasing in [− ,5 − 3].

a) **False**: A function \( f(x) \) is odd if \( f(-x) = -f(x) \). Let's check for \( f(x) = \cos(x) + \sin(x) \):
\[ f(-x) = \cos(-x) + \sin(-x) = \cos(x) - \sin(x) \]
But \( -f(x) = -(\cos(x) + \sin(x)) = -\cos(x) - \sin(x) \). So, \( f(-x) \) is not equal to \( -f(x) \), hence \( f(x) \) is not odd.

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