question_answer

Let function \[f(x)={{x}^{2}}+x+\sin x-\cos x+\log \,(1+|x|)\] be defined over the interval [0, 1]. The odd extensions of f(x) to interval [-1, 1] will be

A)  \[{{x}^{2}}+x+\sin x+\cos x-\log \,\,(1+|x|)\]

B)  \[-{{x}^{2}}+x+\sin x+\cos x-\log \,\,(1+|x|)\]

C)  \[-{{x}^{2}}+x+\sin x-\cos x+\log \,\,(1+|x|)\]

D)  Both (a) and (b)

E)  None of these