10. Let (G, *) be a group, and let H≤ G. Define N(H) = {x € G: x¹ *H* x = H} [Normalizer of H in G]. Show that (a). N(H) ≤G. (b). HAN(H). (c). N(H) = Gif and only if HG. =

Q: Find a closed form representation for the function defined recursively by ƒ(1)=4 and f(n)=3f(x)+n.

A: This is a question of recurrence relation and time of complexity.

Q: 2.11. Let f e r(V), V a variety c A". Define 1 G(f) = {(a1,..., An, An+1) € A"+ |(a1,..., an) E V…

A: If J is any ideal in k[x1, . . . , xn] ,we define Affine Variety as V(J):={ p∈An | f(p)=0 for all…

Q: 4. Find g[h(x)] if g(x) = x² and h(x) = x + 3. %3D O A. x2-- 3 B. x + 6x +9 O C. x + 3x? O D. z + a…

A:

Q: 45. Let g(x) = [x]. Find a) g-¹({0}). c) g-¹({x|0<x< 1}). b) g-¹({-1, 0, 1)).

A:

Q: Let f: (0,1)→ R be a function and let a € (0,1). Match each statement in Group A with a statement…

A:

Q: Let g(x) = e² · (x² – 9), g' (x) = e" . (x² + 2x – 9), and g" (x) = e² · (x² + 4x – 7) , Choose one…

A:

Q: Which of the following functions V: R → R is a Lyapunov function for the respective continuous-time…

A: What is Lyapunov Function: Lyapunov functions are those function satisfying the Lyapunov stability…

Q: Consider the function g(x) = (x - 1)e(1-2) +1, TER. Which of the following intervals makes the…

A:

Q: Prove that, if h is multiplicative function and H is defined by H(m) = Eaim h(d) then H is also…

A: Multiplicative function: A function is said to be multiplicative if , where . Given: The function…

Q: Given that f(x) contains the discrete points of {(0, 3), (1, 4), (2, 0), (3, 1), (4, 2)}, the value…

A: It is given that, function f(x) contains the discrete points of 0,3,1,4,2,0,3,1,4,2. We have to find…

Q: Q3. (a) Let X = {m, n, P, q}, and = {0, X, {m}, {n}, {p, q}, {m, n}, {n,p, q}, {m, p, q}}. Is > a…

A:

Q: Find a closed form representation for the function defined recursively by f(1) = 10 f(n)=2ƒ(%)+n².

A:

Q: 18

A:

Q: Prove this is an equivalece relation. x related to y iff x2 -  y2 is even

A:

Q: 6. Let (a, b, c) and let Σ* be the set of all words w using letters from Σ; see Example 2(b). Define…

A: One to one function: A function f is one-to-one if all element of the range of f corresponds to…

Q: (G) G)- The projection of onto the line through zero 1 is and а. (;) () " () b. C. d.

A: Let u→=11, and the line l through zero v→=00, and w→=1-1. Need to find the projection of u→ onto the…

Q: 5. Find the domain off(z-In(e*-3). Then find f-1 and its domain.

A: f(x) = ln(ex-3)The function "ln" is defined for positive numbers only.Hence, x should be such that…

Q: 8. A function g : Z → Z is defined by g(n) = 3n – 2. Let D be the set of odd integers. (a) Determine…

A: The objective is to solve the above question.

Q: 15.K. Let f be monotone increașing on / [а, б] to R. If c € (a, 6), dehne l(c) l(c) = sup {f(x): I…

A:

Q: u? + 5u – 7 If g(u) In(u) find g'(u)

A: The given function,    g(u)=u2+5u-7ln(u)

Q: 3. Let G be a graph with |V(G)| = 8, such that A(G) = 4. Show that (G)| < 36.

A: The solution is in given below

Q: (a) P (Z'nY') = (Type an integer or a decimal.)

A:

Q: How would you find g (A) if a) g (x) = 1. b) g (x) = (x + 1)2 . c) g (x) =⌊ (2x + 4)/3⌋ Where A =…

A: Disclaimer:  “Since you have asked multiple questions, we will solve the first question for you. If…

Q: 74 t4 - 1 lim t→l t³ – 1

A:

Q: 12. Determine g(G) and c(G) for G = K 2k,4k for a positive integer k.

A: Graph G=Kk,2k,4k denote a tripartite Graph. A graph in which the vertices are partitioned into three…

Q: 5.26 Prove that if G is a graph of order n such that F(G) > (n – 1)/2, then 2(G) = F(G).

A:

Q: If H is a subgraph of G, then show that dg(u,v) <dí(u,v).

A: A graph G illustrates how the vertices and edges are connected. Thus a graph is an ordered pair…

Q: 10. |G/H| [G:H]. *True False

A: 10. True or False: |G/H|=[G:H]

Q: Let H(x):=k for x=, (keN) and H(x):=0 elsewhere on [0,1] Show that H(x) 4ER[0,1].

A: In this question, we use the definition of Riemann integral to check the function H(x) is Riemann…

Q: *) Let p(x) = 8x – 7 and q(x) = /x – 7. Find u(x) given that q(x) = p(u(x)). - и(x) —

A: see 2nd step

Q: 11.2.3 (a) Derive Eq. (11.35) (1-x²) P(x) = (n+1)xPn(x) −(n+1) Pn+1(x). (b) Write out the relation…

A: Let's begin by deriving Eq. (11.35) from the corresponding Legendre polynomials' recurrence…

Q: 2.5. Give an example of a bounded function f and an increasing function a defined on [a, b] such…

A: