Which one of the following is correct? (a) (−2,0]∩[0,2)=∅ (c) (−2,0]∩[0,2)={0} (b) (−2,0]∩[0,2)=(−2,2) (d) (−2,0]∩[0,2)={−2,−1,0,1,2} 2. Let A=(−1,6] and B=[−1,2]. What is A\B ? (a) [2,6] (b) [1,3] (c) (2,6] (d) (1,3] 3. A function is defined as f:D→R, with f(x)=x+2.D is a subset of the reals. The function has range (f)=[1,5]. Which of the following must be D ? (a) [3,7] (b) [1,5] (c) R (d) [−1,3] 4. What is the range of the function f:R→R, with f(x)=e x 2
? (a) (1,[infinity]) (b) [1,[infinity]) (c) (0,[infinity]) (d) R 5. Which of the following is true for any function with domain D, codomain C and range R ? (a) R⊆C (b) R=D (c) R=C (d) R⊆D 1. Three sets are listed below: A=[3,5),B={1,2,3,4,5},C={3k+2∣k∈Z,∣k∣≤2} Draw the sets,(Z∩B)\(A∪C) and (R\A)∩(B∪C) on a number line. Show your working / explain your reasoning where appropriate. 2. Consider the following three objects: - f:R→R,f(x)= x
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- g:R→[0,[infinity]),g(x)=x 2
- h:R→[0,[infinity]),h(x)=(f∘g)(x) Which of these are functions, and why? 3. For each question, either come up with an example of such an object (and explain why it has the desired property,) or explain why no such object exists. (a) Can you find two sets A,B that both contain infinitely many numbers, such that A∩B= {0,1}? (b) Can you find two sets A,B that both contain infinitely many numbers, such that A∪B= {0,1} ? (c) Can you find two sets A,B that both contain infinitely many numbers, such that A\B= {0,1} ?