Question

3) Which of the following is/are group homomorphism(s)? I- $f: (Z,+) \to (Z,+), f(n) = 2^n$ II- $f: (Z,+) \to (Z,+), f(n) = n^2$ III- $f: (R^+, \cdot) \to (R, +), f(x) = \ln(x)$ a) I only b) I and III c) II and III d) III only e) I, II and III f) None

Name: 3 which of the following isare group homomorphisms i f z to z fn 2n ii f z to z fn n2 iii f r cdot to r fx lnx a i only b i and iii c ii and iii d iii only e i ii and iii f none 81435
Uploaded: 2022-02-10T06:17:54-08:00
Duration: 1 min 34 s
Channel: Manik Pulyani
Description: 3 which of the following isare group homomorphisms i f z to z fn 2n ii f z to z fn n2 iii f r cdot to r fx lnx a i only b i and iii c ii and iii d iii only e i ii and iii f none 81435

          3) Which of the following is/are group homomorphism(s)?
I- $f: (Z,+) \to (Z,+), f(n) = 2^n$
II- $f: (Z,+) \to (Z,+), f(n) = n^2$
III- $f: (R^+, \cdot) \to (R, +), f(x) = \ln(x)$
a) I only
b) I and III
c) II and III
d) III only
e) I, II and III
f) None

3 which of the following isare group homomorphisms i f z to z fn 2n ii f z to z fn n2 iii f r cdot to r fx lnx a i only b i and iii c ii and iii d iii only e i ii and iii f none 81435

Added by Cody M.

Calculus: Early Transcendentals

James Stewart 8th Edition

Instant Answer

Solved by Expert Manik Pulyani

02/10/2022

Step 1

Let's check each function: **I- $f: (Z,+) \to (Z,+), f(n) = 2^n$** Here, the operation in both the domain and codomain is addition. We need to check if $f(a+b) = f(a) + f(b)$ for all $a, b \in Z$. $f(a+b) = 2^{a+b}$ $f(a) + f(b) = 2^a + 2^b$ For $f$ to be a Show more…

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3) Which of the following is/are group homomorphism(s)? I- $f: (Z,+) \to (Z,+), f(n) = 2^n$ II- $f: (Z,+) \to (Z,+), f(n) = n^2$ III- $f: (R^+, \cdot) \to (R, +), f(x) = \ln(x)$ a) I only b) I and III c) II and III d) III only e) I, II and III f) None