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 $ ?
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
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.
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.)