CAT 1999 — QA Question 28

F(x) = $\{\begin{array}{lll}0& when& x\le 0\\ -x& when& x>0\end{array}$ and F1(x) = $\{\begin{array}{lll}x& when& x<0\\ 0& when& x\ge 0\end{array}$

Therefore, replacing x by (−x) in above functions, we get

F(-x) = $\{\begin{array}{lll}0& when& x\ge 0\\ x& when& x<0\end{array}$ and F1(x) = $\{\begin{array}{lll}-x& when& x>0\\ 0& when& x\le 0\end{array}$

Clearly, F1(x) = F(−x), hence, option (b) is the correct choice.

Alternate solution:
F1(-2) = −2 = F(2) and F1(2) =0 = F(−2).

So the correct option is (b), i.e. F1(x) = F(−x)

Hence, option (b).