CAT 2004 Question 5

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 5

Which of the following is necessarily true?

Solution

Relation between f3 and f1 would be

$$f_3(x) = -f_1(-x)$$.

Put x= -x we get

$$f_3(-x) = -f_1(x)$$ so multiply by -1 we get

$$-f_3(-x) = f_1(x)$$.



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