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Instructions
Directions for the following two questions:
Answer the questions on the basis of the information given below.
$$f_1(x) = x$$ if $$0 \leq x \leq 1$$ $$f_1(x) = 1$$ if x >= 1 $$f_1(x) = 0$$ otherwise
$$f_2(x) = f_1(-x)$$ for all x
$$f_3(x) = -f_2(x)$$ for all x
$$f_4(x) = f_3(-x)$$ for all x
Question 4
How many of the following products are necessarily zero for every x:
$$f_1(x)f_2(x), f_2(x)f_3(x), f_2(x)f_4(x)$$
Solution
Checking for different values of x . Suppose x= -0.5 we get
$$f_1(x)f_2(x) = 0*0.5 = 0$$
$$f_2(x)f_4(x) = 0.5*0 = 0$$ .
But $$f_2(x)f_3(x)$$ is not equal to zero.
Hence two functions are necessarily equal to zero and two products given above are equal to zero.
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