Functions Question 402

Question: Let $ f_1(x)= \begin{cases} x,0\le x\le 1 \\ 1,x>1 \\ 0,otherwise \\ \end{cases} . $

$ 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?

Options:

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

Show Answer

Answer:

Correct Answer: B

Solution:

[b]