question_answer

Let \[{{f}_{1}}(x)=\left\{ \begin{matrix}    x,0\le x\le 1  \\    1,x>1  \\    0,otherwise  \\ \end{matrix} \right.\]

\[{{f}_{2}}(x)={{f}_{1}}(-x)\] for all x

\[{{f}_{3}}(x)=-{{f}_{2}}(x)\] for all x

\[{{f}_{4}}(x)={{f}_{3}}(-x)\] for all x

Which of the following is necessarily true?

A) \[{{f}_{4}}(x)={{f}_{1}}(x)\] for all x

B) \[{{f}_{1}}(x)=-{{f}_{3}}(-x)\] for all x

C) \[{{f}_{2}}(-x)={{f}_{4}}(x)\] for all x

D) \[{{f}_{1}}(x)+{{f}_{3}}(x)=0\] for all x

Correct Answer: B

Solution :

[b]