CAT 2004 QA Question 22 · Algebra - Functions & Graphs

​​​​​​​

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).