Question 9 (6 points) (2,4, 3) and g (1, 5, 2) are permutations defined on S...
4) [4 marks] Let f be the element of Se defined as follows: f(1) = 3, f(2)= 2, f(3) = 4, f (4) = 1, f(5) = 6, and f(6) = 5. Let g be the element of S& defined as follows: g(1) = 2, 9(2) = 3, g(3) = 1, g(4) = 6, 9(5) = 5, and g(6) = 4. Compute fog and gof.
(1 point) Let f and g be permutations on the set {1, 2, 3, 4, 5, 6, 7}, defined as follows (1 2 3 4 5 6 7 JE (3 1 6 5 7 2 4) f = (1 800 2 5 3 4 4 7 5 3 6 2 7 6) Write each of the following permutations as a product of disjoint cycles, separated by commas (e.g. (1,2), (3,4,5), ... ). Do not include 1-cycles (e.g. (2)) in your...
Two functions g and f are defined in the figure below. 8 2 3 5 6 6 9 9 9 Domain of g Range of g Domain of / Range of Find the domain and range of the composition fog. Write your answers in set notation. Domain of fog : Range of fog : 0 X $ ?
Q= II. Permutations. Consider the following permutations in Sg: 1 2 3 4 5 6 7 8 9 3 1 4 5 9 2 6 8 7 2 7 1 8 4 5 9 3 6 1. Express a and B as products of disjoint cycles. 2. Compute a-108-1 3. Find ord(a) and ord(B). 4. Express a and B as products of transpositions.
9 or 16 (9 complete) X 2.6.53 For f(x)=x +5 and g(x) = 5x +4, find the following functions. a. (fog)(x); b. (gof)(x); c. (fog)(2); d. (gof)(2) a. (fog)(x) = (Simplify your answer.) Enter your answer in the answer box and then click cha
We specific example of two functions that are defined by different rules for formulas) but that are equal as 2. Consider the functions /(x) = x and g(x) = Vr. Find: (a) A value for which these functions are equal. (b) A value for which these functions are not equal. 3. Let A = {1,2,3,4), B = {a,b,c,d,e), and C = {5, 6, 7, 8, 9, 10). Let S : A +B be defined via ((1.d).(2.b), (3, e), (4.a) Let...
Inverses
3. Let g: N\ { 1 } → N be defined by g(n)-the product of the distinct prime factors of n. a. Find g(2,4, 6, 8, 10, 14)) b. Find g(2, 4, 6, 8, 10, 14)) c. Find g (3)) d. Find g'(1)
3. Let g: N\ { 1 } → N be defined by g(n)-the product of the distinct prime factors of n. a. Find g(2,4, 6, 8, 10, 14)) b. Find g(2, 4, 6, 8, 10, 14))...
3. (8 points, 4 points each) f(x)-2x - 1 and g(x)-3x + 4, are functions from R to R. Find a. fog b. gof
Note: For all the questions, provide detailed solution steps. Question 1. For the given functions f(x) = x² and g(x) = 3x2 - 3 (30 points, 6 each) a) fog b) gof c) gog d) fof e) fog (-1) Bonus Question: (10 points, 5 each) Find the Real and the Imaginary Part of the below complex numbers: a) Z1 = 3 - 2i + 34 – 3i) = b) Z2 = (5 -3i). (4-3i) =
1 Given f(x) = 5x² - 4 and g(x) = = 6 - find the following expressions. (a) (fog)(4) (b) (gof)(2) (c) (f o f)(1) (d) (gog)(0) (a) (fog)(4) = (Simplify your answer.) (b) (gof)(2) = (Simplify your answer.) (c) (f o f)(1) = (Simplify your answer.) (d) (g og)(0) = (Simplify your answer.)