Explanation:
F(x) = 1-xwnen0≤x<21when-2<x<0 and F1(x) = -1-xwhen-2<x<0-1when0≤x<2
Therefore, replacing x by (−x) in above functions, we get
F(-x) = 1+xwhen-2<x<01when0≤x<2 and F1(-x) = -1+xwhen0≤x<2-1when-2<x<0
∴ -F(-x) = - 1+xwhen-2<x<01when0≤x<2
= -1-xwhen-2<x<0-1when0≤x-2 = F1(x)
Hence, option (c) is the correct option.
Alternate solution: F1(2) = −1 = F(2) and F1(−2) = 1 = F(−2).
So the correct option is (c), i.e. F1(x) = − F(−x).
Hence, option (c).
» Your doubt will be displayed only after approval.
Help us build a Free and Comprehensive Preparation portal for various competitive exams by providing us your valuable feedback about Apti4All and how it can be improved.