Which of the following functions are homo-morphisms? (a) g: R → M₂(R) given by g(a) =(a ). (b) h: QQ given by f(0) = 0 and00h() (c) f: Z3 Z3 given by f(x) = x³.

Answered: Image /qna-images/answer/85827f1d-489c-4302-ba69-25f1ae4787f8.jpg

Answered: Which of the following functions are…

Algebra & Trigonometry with Analytic Geometry

13th Edition

ISBN:9781133382119

Author:Swokowski

Publisher:Swokowski

Chapter4: Polynomial And Rational Functions

Section4.5: Rational Functions

Problem 50E

See similar textbooks

Similar questions

If a functionfis increasing on (a,b) and decreasing on (b,c) , then what can be said about the local extremum offon (a,c) ?
What is the domain of the function f (x) x2-1 a. (-1,0) U [1, 00) b. (-1,0] U (1, o) c. (-0, –1) U [0,1) d. (-0, –1] U (0,1)
Select the following functions that are bijective. f3: R → R, f(x) = 14 f₂: R → R, f₂(x) 2 f₁:R → R, f₁(x) = x + x + x + x + 4 f4: R → R, f4(x) = -{ = x x², if x 20 X, if x <0
(1) Let f(x) = 1, x > 0 with domf= R++. Find the conjugate of function f(x).
Consider the function f: R → R defined by f(x) = x³ – 3x + 2. = r3 Then (A) ƒ is increasing on the interval (-0, -1), decreasing on the interval (-1, 1), and increasing on the interval (1, 0). | (B) ƒ is decreasing on the interval (-x, –1), increasing on the interval (-1,1), and decreasing on the interval (1, 0). | (C) f is increasing for all x. (D) ƒ is decreasing for all x. (E) none of the other choices is correct
1. Let f: R → R and g: R → R with f(x) = 5x – 7 and g(x) = x² – 4x + 4 Find: a) Domain of .g(D(f.g)) b) Composition function of f
5x+1 14. Prove that the function f: R \ {2} → R \ {5} defined by f(x) is bijective. x-2
2. Let f(x)=x2x3 - 3. a) Find the domain of the function: ○ [-3,00) Ⓒ (-∞0, 3] (-∞0, 3) U (3, 0) (∞, -3) U (-3,00) b) Find the range of the function: (-∞0, 2) U (2,00) ○ [2,00) Ⓒ (-∞, -2] O (-∞, -2) U (-2, 0) c) Is f a one-to-one function? Yes, f is one-to-one. No, f is not one-to-one. d) Use your answer from part c to determine if the inverse of the function f is a function. Yes, the inverse of the function f is a function. No, the inverse of the function f is not a function.
Exercise II.2. let F(.) : R² → R³ and G(): R² → R² be given by (fi(x)) f2(x) f3(x)) y = 9/₁ F(x) = where f1(), f2), f3(-) are as in Exercise II.1(a). The notation is x = (a) x = and G(y) = (2y1 + 3y2 y² + y² 21 I₂ Use the Chain Rule to calculate (FG)'(x) for the various choices of x: - (₁²) (b) x = - (-³₁) (c) x = - (4) (d) x = For reference F1,F2, F3 Exercise II.1. Consider the case n = 2. (a) Find the gradients of the following functions from R2 to R: (i) f₁ (22) := x² + x² − 2 = 4x² + (iii) f3 (ii) f₂ := = 9(x₁ − 1)² + (²+¹)² — 2 (iv) fa x1 X2 (=-¹). I1 In x1 X₂ and −1 == ((x₁ + 1)² + (x₂ −2)²
Prove that the following functions are bijections:(a) f: R → R given by f(x)=ax+b, where a ≠ 0.(b) f: R − {2}→R− {5} given by f(x)= (5x+1)/(x−2)
In(2 – x) x² + y2 – 16 - Determine the domain of the function f(x, y)
Find the relation

SEE MORE QUESTIONS

Recommended textbooks for you

Algebra & Trigonometry with Analytic Geometry

Algebra

ISBN:

9781133382119

Author:

Swokowski

Publisher:

Cengage

Elements Of Modern Algebra

Algebra

ISBN:

9781285463230

Author:

Gilbert, Linda, Jimmie

Publisher:

Cengage Learning,

College Algebra

Algebra

ISBN:

9781938168383

Author:

Jay Abramson

Publisher:

OpenStax

Algebra & Trigonometry with Analytic Geometry

Algebra

ISBN:

9781133382119

Author:

Swokowski

Publisher:

Cengage

Elements Of Modern Algebra

Algebra

ISBN:

9781285463230

Author:

Gilbert, Linda, Jimmie

Publisher:

Cengage Learning,

College Algebra

Algebra

ISBN:

9781938168383

Author:

Jay Abramson

Publisher:

OpenStax

SEE MORE TEXTBOOKS

Which of the following functions are homo- morphisms? (a) g: R→ M₂(R) given by g(a) = (a 6). (b) h: QQ given by f(0) = 0 and h(). (c) f: Z3 Z3 given by f(x) = x³.