CAT Quant Practice Problems

Question: Answer the questions on the basis of the information given below.

\({f_1}\left( x \right) = \left\{ {\begin{array}{*{20}{c}}{x\;;\,{\rm{0}} \le x \le 1}\\{1;x \ge 1}\\{0;\;Otherwise}\end{array}} \right.{\rm{ }}\)

\(\begin{array}{l}{f_2}\left( x \right) = {f_1}\left( { - x} \right){\rm{\; for \;all \;}}x\\{f_3}\left( x \right) = - {f_2}\left( x \right){\rm{\; for\; all\; }}x\\{f_4}\left( x \right) = {f_3}\left( { - x} \right){\rm{\; for\; all\; }}x\end{array}\)

Which of the following is necessarily true?

f4(x) =f1(x) for all x
f1(x) =–f3(–x) for all x
f2(–x) =f4(x) for all x
f1(x) =f3(x) =0 for all x
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