We have the following groups: G: ℝ+ under multiplication H: ℝ under addition we check if log: G→H is isomorphic, first we check homomorphism: log(xy)=log(x)+log(y) by laws of logarithm, next we check if log is bijective, this is where Im stuck, how do I check for bijection in groups? please if able explain step by step in detail, thank you in advance

Q: a) Complete the table of values for the transformed function of f(x) = logx. 1 g(x) = -log(2x + 4) −…

A: The given function  and the transformed function .The objective is to complete the table values and…

Q: +7

A: Since you have asked multiple question, we will solve the first question for you as per our guide…

Q: log(1+e¯*) is The indeterminate form of lim,→∞

A: The form is:-

Q: Let S denote the set of all functions f:{0,1}4 → {0, 1}. Denote by N the number of functions from S…

A: Introduction :

Q: The function g is related to one of the parent functions. g(x) = -(x + 1)³ (a) Identify the parent…

A: Given function is g(x)=-(x+1)3      (1) Solution a: Parent function of (1) is f(x)=x3

Q: The graphs below show functions which are transformations of the basic functions, f (x)% = e" and…

A: To identify the given graph

Q: Use the graphs of f and g below to find the indicated compositions. 6- 5 4 321 3+ 2+ -1 0 1 2 3 4 1.…

A:

Q: What transformations take the graph of ƒ(x) = eª to ƒ(x) = −eª — 2? -

A:

Q: f(x) = x² and g(x) = (x + 1)² — 12 - reflection across the y axis reflection across the x axis right…

A:

Q: Write a rule for g and then graph each function. 1. f(x)-x-x- 1; g(z) = 0.3f(x) %3D

A: As gx=afx then the graph will either stretch or compress. If gx=fx-a then graph will shift a units…

Q: FUNCTION 1 Parent Function: e.g f(x)=√x, f(x) = b*, f(x) = ²/ Equation of the transformed function:…

A: Task: Take any function f(x)=x, bx, sinx etc... and Apply transformations like a vertical stretch,…

Q: shifted right 3 units and shifted down 4 units. O f(z) = Va + 3 - 4 O f(z) = VI -3- 4 O f(z) = Vz +…

A: You need to have the basic idea of transformations of graph. For shift in right direction there…

Q: Create your own exponential function such that the following conditions are satisfied. Graph your…

A: We will keep all the conditions in mind to generate our exponential function.

Q: A degree three polynomial function F is graphed. What is f(x)?

A: Given:Graph x,y=1,-18

Q: Describe the transformations from the parent function, then graph: x+4 -2 f(x)= 3 Domain: (-00,00)…

A: Given problem:- f(x)=(1/3)x+4-2  Describe the transformations from the parent function, then graph

Q: 6) Find the resulting function after the following transformations are applied to the graph of h(x):…

A:

Q: Consider these functions: f(x) = 3 and g(x) = 3+2-5

A: Given,          f(x)=3x,   and     g(x)=3x+2-5

Q: que de la fonction g(x) = -log₂ x + 2 ▪n f(x) = log₂ x. Explique les transfor de f(x) pour obtenir…

A: Given the functions f(x)=log3x and g(x)=-log3x+2.

Q: Name HW Math 115 Fall 2019 Group # Problem 4- Revisiting Composition of Functions: Refer to the 3…

A: Here the given 3 functions are f(x) = 2 x - 3 , g(x) = |x+2| - 7 and h(x) = 7x+4-1. In part (a)…