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)
Pick one
A) 0  B) 1  C) 2  D) 3  E) 4
Explanation :   We have to consider positive and negative numbers for all the cases.   f1(x) is positive for positive numbers, and 0 for negative numbers. (0 for x = 0)   f2(x) is 0 for positive numbers, and positive for negative numbers. (0 for x = 0)   f3(x) is 0 for positive numbers, and negative for negative numbers. (0 for x = 0)   f4(x) is negative for positive numbers, and 0 for negative numbers. (0 for x = 0)   So, we see that, out of the 3 products in the question, f1(x)*f2(x) and f2(x)*f4(x) are always zero, for any x.   Answer : 2
<result>C</result>
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)