1. Let A = {a, b, c}, B = {1,2,3}, C = {x, y, z, w}, D = {4,5, 6}. Let the functions f : A → B, g : B → C, h : C → D be defined by: f = {(a, 2), (b, 1), (c, 2)} g = {(1, y), (2, x), (3, w)} h = {(x, 4), (y, 6), (z, 4), (w, 5)}. Determine if each function is: (a) Onto (b) One-to-One

Q: 31. Let f(x) = [x²/3]. Find f(S) if a) S= (-2,-1, 0, 1, 2, 3). b) S = {0, 1, 2, 3, 4, 5). c) S = {1,…

A: The given function is, fx=⌊x2/3⌋. To Find: f(S) for the following set S, (a) S=-2,-1,0,1,2,3 (b)…

Q: 4) Solve the following linear system or indicate the nonexistence of solution. X1 – 2x2 + 5x3 – 3x4…

A: Or, take x2 = k Hence, solution of the system is x1 = 1+2k, x2 = k, x3 = 1, x4 = 2

Q: 18. For what value of x will make the relation {(2,5), (9, 7), (x – 7,9), (18, 11)} a function? 16…

A: We find the value of x that will make the relation {(2,5), (9,7), (x – 7,9). (18, 11)} a function.

Q: Let C = {0, 1, 2, 3} and f: C → C, g: C → C with ƒ = {(0, 2), (1, 2), (2, 3), (3, 0)}, {(0, 3), (1,…

A:

Q: 1. The map T : Mat2,2(R) → Mat2,2(R) given by a +c d a b T c d а — d

A:

Q: X = {p, q, r, s} Y = {4, 5, 6, 7, 8} The function f: X → Y is defined as: f = {(s, 8), (r, 8), (q,…

A: We want to find elements in the range of function f.

Q: Let A = {1,2,3}, Define the functions f: A → C and g: B → C by f(1) = 7, f(2) = 9, f(3) = 7, g(4) =…

A:

Q: Two sets A and B are defined as follows: A = {x, y, z); B = {1, 2, 3}. Ug Oh f range of g range of h…

A:

Q: Let A = {1,2,3}, B B = = Define the functions f: AC and g: B → C by f(1) = 7, f(2)= 9, f(3) = 7,…

A: We want g o h = f.     So, we want g o h(1) = f(1) = 7            and g o h(3) = f(3) = 7   Now,…

Q: R(s, t) = G(u(s, t), v(s, t)), where G, u, and vare differentiable, and the following applies. v(7,…

A: Given that

Q: Let R(s, t) = G(u(s, t), v(s, t)), where G, u, and v are differentiable, and the following applies.…

A:

Q: X = {p, q, r, s} Y = {4, 5, 6, 7, 8} The function f: X→ Y is defined as: f = {(r, 7), (s, 8), (p,…

A:

Q: Supposer is an invertible function with domain [1, 5] and range [2,7]. Then the domain of r−¹(x − 1)…

A: Given that r is an invertible function with domain [1,5] and range [2,7].It means that for every…

Q: 5. Let D = {1, 2, 3, 4, 5}, C = {a, b, c, d}, and g = {(1,a), (2,c), (3,d), (4,c)}. Determine…

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Q: {h,p,t, v, w}, and 7, 10, 12, 15, 16, 21, 24, 29, 30}. 21), (р, 29), (t, 24), (v, 24), (w, 10)} de n…

A: We have to complete the given statement according to the given information

Q: Let R(s, t) = G(u(s, t), v(s, t)), where G, u, and v are differentiable, and the following applies.…

A: Given that  where G,u and v are differentialblle functions

Q: 3. Write the mapping rule for this function a) y = - 3f[-4(x - 1)] + 2: (x, y) → + d, ay+ b) f(x)=…

A:

Q: 3. If f:(X,r)(Y.A) and g:(Y,A)→(Z,r) are open functions, prove that gof :(x.r)(Z.r) is open…

A: Definition: An open map is a function between two topological spaces that maps open sets to open…

Q: 10.37. Let A ={1,2,3,4}, B={a,b,c} and C = {w, x, y, z} . Consider the functions f : A → B and g: B…

A: Thanks for the question :)And your upvote will be really appreciable ;)