Question 3*. Let S = {1,2,3, 4}, and let f : S → S, g : S → S and h : S –→ S be the following functions. f = {(1,3), (2, 1), (3, 4), (4, 2)}, g = {(1,2), (2,4), (3, 4), (4, 3)}, h = {(1,2), (2, 2), (3, 2), (4, 2)}. (a) For each of the functions f, g, h determine, with justification, whether it is (i) injective; (ii) surjective; (iii) bijective; or (iv) none of these. (b) Determine the range (or image) of each of the functions f, g, h. (c) Determine which (if any) of the functions f, g, h is invertible. (Note that invertible means having an inverse.) For any that are, calculate the inverse. (d) Calculate the compositions f o f, ƒ o g and go f. (e) Calculate (ƒ oh) o g and fo (h o g) and verify that they are equal.

Question 3*. Let S = {1,2,3, 4}, and let f : S → S, g : S → S and h : S –→ S be the following functions. f = {(1,3), (2, 1), (3, 4), (4, 2)}, g = {(1,2), (2,4), (3, 4), (4, 3)}, h = {(1,2), (2, 2), (3, 2), (4, 2)}. (a) For each of the functions f, g, h determine, with justification, whether it is (i) injective; (ii) surjective; (iii) bijective; or (iv) none of these. (b) Determine the range (or image) of each of the functions f, g, h. (c) Determine which (if any) of the functions f, g, h is invertible. (Note that invertible means having an inverse.) For any that are, calculate the inverse. (d) Calculate the compositions f o f, ƒ o g and go f. (e) Calculate (ƒ oh) o g and fo (h o g) and verify that they are equal.

Advanced Engineering Mathematics

10th Edition

ISBN:9780470458365

Author:Erwin Kreyszig

Publisher:Erwin Kreyszig

Chapter2: Second-order Linear Odes

Section: Chapter Questions

Problem 1RQ

See similar textbooks

Similar questions

ab Let f and g be functions defined as follows: 2 ƒ = {( − 19, − 2), ( – 18, − 1), ( – 17, 3). (- 16, ₂).(-15,3)} 3 9 = {( − 18 19,- -7).(-18, 1). (-17, 3). (-16, ).(-15,0)} 4 10 Compute the indicated value. If the value does not exist, enter DNE. (i) (g+g)(15) = (ii) (fg)(16) = (iii) (ff)(19) = (iv) (4) 18) = > Next Question G Search or type URL ← % 6 esc 1 Q @ 2 W #3 Q E D $ 4 R 5 T
The range of the inverse of the function f = {(1,4), (2,9), (3,14), (4, 18)} is O {1, 2, 3, 4 } O (4, 9, 14, 18} O {(4,1), (9,2), (14,3), (18,4) } O { (2,9), (3,14), (4,18) } { (1,4), (2,9), (3,14) }
Answer question 2
4. Does the function represented by the set {(1, 2), (2, 3), (3, 4), (4, 8), (5, 10)} represent an invertible function? If yes, list the corresponding set of z- and y-values for the inverse function. O Yes, the set represents an invertible function. The corresponding set of a- and y-values for the inverse function is {(2,1), (3, 2), (4, 3), (8, 4), (10, 5)}. O No, the set does not represent an invertible function. O Yes, the set represents an invertible function. The corresponding set of z- and y-values for the inverse function is{(2, –1), (3, –2), (4, –3), (8, –4), (10, -5)}. O Yes, the set represents an invertible function. The corresponding set of a- and y-values for the inverse function is{(-1, -2), (–2, –3), (-3, –4), (-4, –8), (–5, –10)}. 9 Type here to search
Back Question 10 Not yet answered Marked out of 1.00 P Flag question r\pq 00 01 11 10 0 1 111 1 The functions presented in the digital form(s) of the Kamaugt diagram is/are: a. V(1,2,3,5). Ob. (0,4,6,7) Oc. (1,2,3,5,6) Od. V(0,4,7) Previous page 13
6.) Suppose f and g are inverse functions. Consider the table below. X f(x) -1 ƒ˜¯¹(x) -5 12 -4 Ans: -1 10 -1 2 0 9 -2 Write an equation for the line tangent to g(x) at x=4 . 1 4 -2 2 0 -1 4 -2 -5 5 -7 0
2. U = {11,22, 33, 44, 55}. V = {1,2,3, 4}. uRv if and only if u – v is diagram for R. Is Ra function? even. Draw an arrow
1. Suppose that five Math 310 students, whom we'll label Students A, B, C, D, and E, achieve the following scores on the first midterm, second midterm, and final exam: Student | Midterm 1 Midterm 2 Final (u) 76 (v) 48 (y) 43 A B 92 92 90 C 68 82 64 D 86 68 69 E 54 70 50 Find the function of the form y = Bo+ Biu+B2v that best fits these data, using least squares. (You are strongly encouraged to use technology, such as WolframAlpha, to compute any necessary matrix products and inverses.) (b) scores 72 on the first midterm and 58 on the second? (Round to the nearest integer.) What score y on the final exam does your formula predict for a hypothetical Student F who Problem 1 asks you to model the dependence of one number (the final exam score) on two others (the scores on both midterms). You are therefore finding not a line of best least-squares fit, but a plane, as described in section 6.6 of the textbook under the heading “Multiple Regression".