9) What does the mathematical symbol Il represent? 10 Let X = (1, 3, 5) and...
Let X = {1, 3, 5) and Y = {a,b,c,d). Define g: X→Y by the following arrow diagram. (a) Write the domain of g and the co-domain of g.
3 1 3 -4 (a) Write a set of ordered pairs (x, y) that defines the relation. (b) Write the domain of the relation. (c) Write the range of the relation. (d) Determine if the relation defines y as a function of x.
R × R | x < y} . This means that R 10. Let R< = {(x, y) relation on R. is the "less than" 95 (a) What is the domain of the relation R<? (b) What is the range of the relation R<? (c) Is the relation R a function from R to R? Explai. Note: Remember that a relation is a set. Consequently, we can talk about one relation being a subset of another relation. Another thing to...
please show work 1.Let g(x) = log3(x +3)-1 . d. (3 pts) f(8)-3, the corresponding point on the graph of f(x)is.H The transformed point on the graph of g(x) is . e. (2 pts) Find the domain and the range. Write in interval notation. 1d. point on f(x): point on g(x): f. (1 pt) What is the vertical asymptote? That is, as x→ 1e. D: R: 1f. 8. (5 pts) Find the equation of the inverse, g(x). 1g. 1.Let g(x)...
Please answer the following questions with solution, thanks 4. Consider the function f(x) = 2x + 1, a) Find the ordered pair (4. f(4) on the function. b) Find the ordered pair on the inverse relation that corresponds to the ordered pair from part a). c) Find the domain and range of f. d) Find the domain and the range of the inverse relation off. e) Is the inverse relation a function? Explain. 5. Repeat question 4 for the function...
10. [4] Let R be the relation on the set {0, {f}, {y}, {x,y}} defined by R= {(S, T): SUT|=2} (a) Represent the relation R as a set of ordered pairs. (b) Represent the relation R as a relational digraph.
This is discrete mathematics. I need answer and explanation for #28 #29 #30. Thank you so much!! 28. Define an "onto" function. Give an example of an onto function from X = {1,2,3,4,5,6,7,8,9,0} onto Y = {a,b,c,d} 29. What is the domain and co-domain of the function which assigns to each pair of non- negative integers the first integer of the pair? What is the range? 30. Let S be the set of all positive integers not exceeding 100. Let...
(b) Let F, G and H be the following sets of ordered pairs F {(1,1), (2, 2), (3,7), (4,1)} G {(1,1), (2, 1) (3, 2), (3,3), (4,2)} н 3 {(1,1), (2, 3), (3, 4), (4, 2)} (i) Does F define a function f :{1,2,3,4} (ii) Does G define a function g : {1,2,3,4} (iї) Does H define a function h : {1,2,3,4} —> {1, 2, 3, 4}? (iv) For those of f, g and h that are functions, write down...
Question4 please (1). Let f: Z → Z be given by f(x) = x2. Find F-1(D) where (a) D = {2,4,6,8, 10, 12, 14, 16}. (b) D={-9, -4,0, 16, 25}. (c) D is the set of prime numbers. (d) D = {2k|k Ew} (So D is the set of non-negative integer powers of 2). (2). Suppose that A and B are sets, C is a proper subset of A and F: A + B is a 1-1 function. Show that...
1. Let A= {0,1}2 U... U{0,1}5 and let < be the order on A defined by (s, t) E< if and only if s is a prefix of t. (We consider a word to be a prefix of itself.) (a) Find all minimal elements in A. (Recall that an element x is minimal if there does not exist y E A with y < x.) (b) Are 010 and 01101 comparable? 2. Give an example of a total order on...