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?

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

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

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

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

Let \[{{f}_{1}}(x)=\left\{ \begin{matrix} x,0\le x\le 1 \\ 1,x>1 \\

1.	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
Answer» C. \[{{f}_{2}}(-x)={{f}_{4}}(x)\] for all x

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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?

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