Let X = {1, 3, 5) and Y = {a,b,c,d). Define g: X→Y by the following arrow diagram.
(a) Write the domain of g and the co-domain of g.



Let X = {1, 3, 5) and Y = {a,b,c,d). Define g: X→Y by the following arrow diagram.
9) What does the mathematical symbol Il represent? 10 Let X = (1, 3, 5) and Y = {a,b,c,d). Define g: X by the following arrow diagram. Y . a. Write the domain of g and the co-domain of g. b. Find g(1), :.! c. What is the range of g? d. Is 3 an inverse image of a?" e. What is the inverse image of b? 1. Represent g as a set of ordered pairs.
(1,3), с %3D (2,1), d (3,4) (1,2), b (4,2), f (5,3) and (5,5). Let 5. Let a = е 3 - {a, b, c, d, e, f, g} be the set of these 7 points. We define the following partial order on S: We have (r, y)(', y) iff x< x and y < / Draw the Hasse diagram of S S 6. We consider the same partial order as in Problem 5, but it is now defined on R2....
Let B C R" be any set. Define C = {x € R" | d(x,y) < 1 for some y E B) Show that C is open.
12. Let g(x), h(y) and p(z) be functions and define f(x, y, z) = g(x)h(y)p(2). Let R= = {(x, y, z) E R3: a < x <b,c sy <d, eszsf} where a, b, c, d, e and f are constants. Prove the following result SS1, 5100,2)AV = L*()dx ["Mwdy ['Plzdz.
Problem 6.8. Let X = {1, 2, 3}, Y = {a, b, c, d, e}. (a) Let f : X → Y be a function, given by f(1) = a, f(2) = b, f(3) = c. Prove there exists a function g : Y → X such that g ◦f = id X . Is g the inverse function to f? (Hint: define g on f(X) to make g ◦ f = id X . Then define g on Y...
please show work
1.Let g(x) = log3(x +3)-1 . d. (3 pts) f(8)-3, the corresponding point on the graph of f(x)is.H The transformed point on the graph of g(x) is . e. (2 pts) Find the domain and the range. Write in interval notation. 1d. point on f(x): point on g(x): f. (1 pt) What is the vertical asymptote? That is, as x→ 1e. D: R: 1f. 8. (5 pts) Find the equation of the inverse, g(x). 1g.
1.Let g(x)...
Question 3. Let 3 5/' and for x(2),y -(,) ER2 define (a) Show that the assignment (x, y) > (x,y) defined ın (1) us an nner product [10 marks (b) If a - (1,-1) and b - (1,1), then show that the vectors a and b are lınearly ndependent but they are not orthogonal with respect to the inner product n (1) 3 marks] (c) Given the vectors a and b in (b), the set (a, by is hence a...
3. (i) Let f(x) = 2x4 –1 +5 and d(x) = 22 – 24 – 1. Use the long division to divide f(x) by d(x). Write out the long division diagram, and then write your final answer in the form f(x) = d(x)g(x) +r(x), where g() is the quotient, and r(x) is the remainder. (ii) Let f(x) = 3x - x2 + 2x + 30 and d(x) = x +2. Use the synthetic division to divide f(x) by d(x). Write...
Part C: Communication (20 marks) 1. Let f(x) = x + 3 and g(x) = x2 + 8x + 15. (5 a) Determine an equation for the combined function Y = F(X) marks) ico g(x) nobela bom a) State the domain and range (5 marks) 1200 to b) Sketch a graph of the function (5 marks) 410 e add (a bor AS PAGE 5 DA
3) Let X, Y be vector fields. For all functions f, define the commutator X, Y]0=X(Y()-Y(X(f). Show that X, Y=Z is a vector field, by verifying that it satisfies sum rule and product rule: Z(f+g)-Z(+Z(g) Zfg)-fZ(g)+gZ(). Extra credit: write /X, YJ in local coordinates.