Discussion

Question:

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

f₁(x)f₂(x), f₂(x)f₃(x), f₂(x)f₄(x)?

Explanation:

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).

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