CAT 2004 — QA Question 23
Composite FunctionsEasy
Passage / Data
Answer the following question based on the information given below.
f1(x) = x 0 ≤ x ≤ 1
= 1 x ≥ 1
= 0 otherwise
f2(x) = f1(–x) for all x
f3(x) = –f2(x) for all x
f4(x) = f3(–x) for all x
Which of the following is necessarily true?
Answer & solution
- A
f4(x) = f1(x) for all x
f1(x) = –f3(–x) for all x
- C
f2(–x) = f4(x) for all x
- D
f1(x) + f3(x) = 0 for all x
Solution
From the table in the previous question,
–f3(–x) = –f4(x) = f1(x).
Hence, option (b).