Let A and B be two sets and f be function. f: A B.Assuming the function f is invertible, what is the domain of f O 1UB O AB

Q: Consider the functions f : A → B, g : B → A and h : B → A such that if gf = 1A and fh = 1B. Prove…

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Q: Consider the functions f : A → B, g : B → A and h : B → A such that if gf = 1 Ą and fh = 1B. Prove…

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Q: . Consider the functions f : A → B and g : B → C. a) If f and g are both injective, show that g o f.…

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Q: Let f: XY and A,BCX. Give an example of a function f and sets A and B that f[A\B] #f[A]\f[B]

A: Take any constant function and subsets A and B such that they overlap.

Q: Give an interval over which the set of two functions fi(x) = x² and f2(x) = x |x| is linearly…

A: Given: The set of two function.f1(x)=x2f2(x)=xx

Q: Which of the following function f: Z x Z Z is not onto? 2020 a. f(a, b) = a b. f(a, b) = lbl c. f(a,…

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Q: Suppose that the functions u and w are defined as follows. u (x) =-x+2 w (x) = -2x? Find the…

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Q: If f is a function from X to Y and C, D are subsets of Y then A O f(C-D) =f(C)-f (D) B f'(Cn…

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Q: Determine whether the function f : Z × Z → Z is onto if a) f (m, n) = m + n. b) f (m, n) = m2 + n2.…

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Q: Let f: A-XX Y be defined as f (a) = (f, (a). f2 (a)) each a A, Then f is continuous if and only if…

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Q: Let F(x) = f(x*) and G(x) = (f(x))* and suppose that %3D %3D a = 3, f(a) = 2, f'(a) = 8, f'(a*) = 11…

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Q: Let f(x) = ax + b and g(x) = cx^2 + dx, where a, b, c, and d are constants. Compute f o g and g o  f…

A: We have to find fog and gof.

Q: Show that if f and g are linear functions such that f(O) = g(0) and f(l) = g(l), then f = g.

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Q: Suppose that the functions u and w are defined as follows. u(x) =x²+6 w(x)% =D/x+1 W Find the…

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Q: Let f(x, y) = x²y. Compute and simplify each of the following: (a) f(x + h, y) – f(x, y), and (b)…

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Q: Let f(x) = (ax + b) / (cx + d) .…

A: Given: fx=ax+bcx+d

Q: Let f.g.h:A - A be any bijective functions. Then (g oh on-

A: (g∘h∘f)-1=f-1∘h-1∘g-1 composition of function is associative…

Q: Let r(x) = f(g(h(x))), where h(1) = 4, g(4) = 6, h'(1) = 3, g'(4) = 5, and f '(6) = 8. Find r'(1).…

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Q: (a) Let the function g : Z → Q be given by the rule 2n° +3 g(x) n2 + 1 Justifying your answers, say…

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Q: Let f C D be a function, with C being the domain and D being the codomain. Show that for any C₁, C₂…

A: Functions

Q: 2. Let a = (a1,..., an) € R" and let f : R" →R be defined by f(x) = (a, x). Compute the following:…

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Q: Show that if f and g are linear functions such that f (0) = g(0) and f (1) = g(1), then f = g.

A: Given: f and g are two linear functions where: f0=g0……1f1=g1……2   To prove: f=g

Q: Suppose that the functions u and w are defined as follows. u (x) = 2x+2 w (x) =x² – 2 Find the…

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Q: Let ø be a C' function, and suppose 00 $(x) = >, b,Un(x)., ø"(x) = ), cnUn(x). %3D n=1 =1 Express…

A: Here in the question it is give that ϕ is a C1 function .  Consider the given function as follow:…

Q: Let r(x) = f(g(h(x))), where h(1) = 2, g(2) = 3, h'(1) = 4, g'(2) = 3, and f'(3) 7. Find r'(1) %3D…

A: Recall: The derivative of a composition is the product of the derivative of the outer function (…

Q: Suppose that the functions u and w are defined as follows. u (x) = -x-1 w (x) = -2x²+2 %3D Find the…

A: The given function is ux=-x-1 and wx=-2x2+2

Q: Let a, b, c, d ∈F. Prove that the function δ: M2×2(F) →F defined by δ(A) =…

A: Let a,b,c,d belongs to F.Then it is required to prove that the function is linear function.

Q: Suppose that the functions u and w are defined as follows. u (x) = x² +9 w (x) = /x+ 8 Find the…

A: To find the functions

Q: Suppose that the functions u and w are defined as follows. u (x) = 2x+2 w (x) =x²-2 Find the…

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Q: Suppose that the functions u and w are defined as follows. u (x) = 2x+5 w (x) =x+4 Find the…

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Q: Suppose that the functions u and w are defined as follows. u (x) =-2x+2 w (x) =x² – 1 Find the…

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Q: Let X, Y be sets and f : X → Y . Prove f-1(An B) = f¬1(A)nf-²(B). For any A, B CY.

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Q: I. Let f(x) = 2x - 1, g(x) = 3x, and h(x) = x² + 1. Compute the following: %3D 1. f(g(-3)) 2.…

A: “Since you have asked multiple question, we will solve the first question for you. If you want any…

Q: Let A = {a, b, c, d, e}, B = {1, 2, 3, 4, 5} and let f: A B, f(a) = 5, f(b) = 2, f(c) = 3, f(d) = 1,…

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Q: 6. Let A and x be defined as A = X%3D %3D 9. and define the function f(x) = x" Ax. %3D (i) Show that…

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Q: Determine the values of m and b such that function g is continuous at every real number: if r 1.

A: Since the function g is continuous.So, limx→1-g(x)=g(1)limx→1-x2-mx=-212-m(1)=-2m=1+2m=3

Q: Let F(x) = f(x*) and G(x) = (f(x))ª and suppose that a = 8, f(a) = 2, f'(a) = 9, f (a*) = 14 %3D…

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Q: Let f : S → T be a function, and let A and B be subsets of T. Prove or give a counterexample to the…

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Q: Let A = {1,2,3} and B = {x,y}. %3D %3D (a) How many functions are there from A to B? (b) How many…

A: Given that                 A=1, 2, 3   and B=x, y We have to find in how many functions are there…

Q: Suppose that the functions u and w are defined as follows. u (x) =x²+6 w (x) = /x+9 %3D Find the…

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Q: Let f : D → E be a function and let A C D, BC E. Prove the following: (a) f(f-1(B)) C B. (b) If f is…

A: The function is f:D→Eand A⊆D and B⊆E

Q: Let f, g : R→R be defined, respectively by f(x) = x + 1, g(x) = 2x – 3. Findf + g, f – g and f/g.

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Q: Consider the functions f : A → B, g : B → A and h : B → A such that if gf =14 and fh = 1B. Prove f…

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Q: There is a number c in the interval (a, b) such that f ′ (c) = 0.

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Q: the domain of the function : y = In(x² + x + 1) is [0,0) Select one: O True O False

A: From the given problem:   y=lnx2+x+1   We know that logax is defined when x,a>0.

Q: Let g : R → R be the function g(t) = t, and let B = [-3, 1] U [2, 3]. Express the set g(B) as an…

A: First observe the behavior of the given function  g(t)=t2 : Domain of the function is ℝ and range…

Q: Suppose that the functions u and w are defined as follows. u (x) =-x-1 w (x) =? %3D Find the…

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Q: Let A = {a, b, c, d, e}, B = {1, 2, 3, 4, 5} and let f : A → B, f(a) = 5, f(b) = 2, f(c) = 3, f(d) =…

A: See the attachment

Q: Let B = R − {3}. Define g : B → B by g(t) = 3t/(t − 3) Show that the function g is injective.

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