Discrete Mathematics

1. Why is f not a function from R-to-R if a) f(x)=1/x ? b) f(x)=x ? 2. Give an example of a function from N to N that is a) one-to-one but not onto. b) onto but not one-to-one. 3. What is the term a8 of the sequence {an} if an equals a) 2n1 ? b) 7? 4. Determine whether each of these functions is a bijection from R to R. a) f(x)=2x+1 b) f(x)=x2+1 c) f(x)=x3 5. is f(x)=x3+1 have an inverse? If so, Find the inverse function of it. 6. Find 4j=0j !, Find 4j=0j !. 7. A=[1122]. d) Use your answers to (b) and (c) to show that (A1)3 is the inverse of A3. 8. Let A=[110110], and B=011011 Find a) A B. b) AB. c) A B. 9. Let R be the relation {(1,2),(1,3),(2,3),(2,4),(3,1)}, and let S be the relation {(2,1),(3,1),(3,2),(4,2)}. Find SR