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CAT 1999 — QA Question 29

Even / Odd FunctionsEasy
Passage / Data

Answer the next 4 questions based on the following information.

In each of the following questions, a pair of graphs F(x) and F1(x) is given. These are composed of straightline segments, shown as solid lines, in the domain x ∈ (−2, 2).

Choose the answer as

a. if F1(x) = –F(x)
b. if F1(x) = F(–x)
c. if F1(x) = –F(–x)
d. if none of the above is true

Answer & solution

Answer: 3

Solution

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).

CAT 1999 QA Q29: — Solution | TheCATExam