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CAT 2004 — QA Question 22

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

How many of the following products are necessarily zero for every x

f1(x)f2(x),  f2(x)f3(x),  f2(x)f4(x)?

Answer & solution

  • A

    0

  • B

    1

  • 2

  • D

    3

Solution

​​​​​​​

f1(x) = x                  0 ≤ x ≤ 1
         = 1                 x ≥ 1
         = 0                 –1 ≤ x < 0
         = 0                 x ≤ –1

The table is written after defining the given function as above.

From the table, only f1(x) × f2(x) and f2(x) × f4(x) are necessarily zero for every x.

Hence, option (c).

CAT 2004 QA Q22: How many of the following products are necessarily zero for every x f 1 ( x ) f 2 ( x ), f 2 ( x ) f 3 ( x ), — Solution | TheCATExam