Let f:Z → Z be defined by f (x) = 2x + 1 where x € Z. Is f a one to one correspondence (bijection)?

Q: Let F(x, y, z) = y° z°i+ 2xyz³j+ 3xy° z²k. (a) Find the domain of F, and show that F is…

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Q: 5. Determine whether the function f : R+ → R defined by the rule f (x) = positive real numbers x in…

A: A function is said to be bijective if the function is both one one and onto. The given function is…

Q: Let f : R R with f(x) = -2x +5 Prove that f is onto.

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Q: Let f : (0, ∞) → R be defined by f(x) = ln x. Prove that f is onto.

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Q: Let f: R - R be defined by f(x) = |x+2, r20 interval ]1, 3[ under f) is (a) ]3, 5[U] – 1, 1[ (b) (0.…

A: given that,  f(x)=x-2, x<0x+2, x≥0

Q: Let A={x e R|-1sx s1} = B, Show that f:A →B given by f (x)=x|x| is a bijecti on.

A: we have to show that given function is bijective

Q: Define F: R x R → R × R as follows: F(x, y) = (3y – 1,1 – a) for all (x, y) in R × R. (a) F(0,0) = ?…

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Q: Consider the functionf defined by f(x,y) = k. Use the definition to show that for fixed real numbers…

A: We are given that f(x, y) = k and a, b, c, and d are fixed real numbers with a<b and c<d.…

Q: (a) Prove the following relation: B(x + 1, y): B(x,y) x + y %3D

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Q: Prove that the multiplication map · : ℤ/n × ℤ/n → ℤ/n given by [x] · [y] = [xy] is well-defined.

A: A multiplication operation defined on ℤ/nℤ×ℤ/nℤ→ℤ/nℤ as                x·y=xy

Q: .

A: Let L be the linear operator on R3 defined by

Q: Exercise 3 Define f : Rª\{0} by f(r) = |r|,'. Using the e-5-definition, prove that f is continuous.…

A: We are given a function f whose domain is ℝd-{0}. The function f is defined as  f=x2-1. Where…

Q: Please solve this question.

A: We are given that L(p(x)) = p(0). Let p(x), q(x) in P4(F) and α, β in the field F. Now,…

Q: Let R be the relation on N defined by x Ry if x and y share a common factor other than 1. Determine…

A: The relation R is defined by xRy if x and y share a common factor. We need to check reflexivity and…

Q: Exercise 3. Show that f : Z → N so that f (z) = z² + 1 for all z E Z is neither one-to-one %3D nor…

A: One-One Function: A function is said to be One-One if for every element in the domain there exists…

Q: Give the relation R induced by the partition above on A.

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Q: Let X be any set and let Y = "2¬X = {x : X → {0, 1}}, that is, Y is the set of all functions from X…

A: To prove that F is a bijective mapping,we have to show that it is both one-to-one and onto.

Q: Let R be the relation on R defined by R= {(x, y) E R × R | x² + y² = 4 or x = y²}. Answer each of…

A: Given that R be the relation on ℝ defined by,R=x,y∈ℝ×ℝx2+y2=4 or x=y2

Q: T is a function?

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Q: Define a bijection function f : N → {n : n > 10, n e N}, and prove it.

A: We have to define a bijection function f:N→n:n≥10,n∈N and prove it. Define a function…

Q: 3) Prove that the multiplication map · : Z/nx Z/n → Z /n given by [x] · [y] = [xy] is well-defined.

A: To prove that the multiplication map · : ℤn×ℤn→ℤn given by    x·y=xy  is well-defined.

Q: Prove that the function : R-{1} →R- {2} defined by 2a f(x)= s bijective. 2 1

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Q: Let L be a linear operator on R1 and let a = L (1). Show that L (x) = ax for all x ∈ R1.

A: It's a highly simple question.

Q: 1. Show that the following maping f are linear: f : R² → R² defined by f(x, y) = (x+ y,x).

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Q: Let f:A→B. Prove that if X⊆A and f is injective, then f(A−X) =f(A)−f(X)

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Q: Let f : R −→ R be defined by f(x) = 2 − 5x. Show that f is bijective, and find (f^(−1))(x).

A: A function f is bijective if f is one- one  and onto

Q: Show that the function f: Real #s to Real #s defined by f(x)=x2 is not a homomorphism.

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Q: Let f:Z x Z+ Z x Z be the function given by f(z, y)= (2z + y,I- y). Find, with proof, an element af…

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Q: 4. Define f:R → R, define f (x) = 3x + 5 for all x e R. Show that a. fis one - to - one; b. f maps R…

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Q: Compute the norms for (a)||f(1)||, (b) ||F(x)|l2 (c)||f(x)||, where f(r) = -VI-r, defined on [0, 1).

A: Given- fx =-1-x defined on [0, 1] (a) we have to calculate fx  fx=∫01fxdx        =∫01-1-xdx…

Q: Prove that f : R → R by f(x) = 2x+4. Prove that f is one-to-one and maps surjectively onto R.

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Q: Let X be any set and let Y = 27X - {x : X {0, 1}}, that is, Y is the set of all functions from X to…

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Q: Let A = {u, v, w}, B = {x, y, z}. Determine whether the relation R = {(u, x), (v, z), (w, y)} from A…

A: In R from A to B is an injection function as well as a surjection function.

Q: Prove A = BH (x)A = (Vx)B without using the equivalence theorem.

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Q: Let R be the relation on N defined by x R y if x and y share a common factor other than 1. Determine…

A: The relation R is defined as xRy on natural numbers Nsuch that x and y share a common factor other…

Q: Prove or disprove whether the function f (r) = a +2 is a bijection from R R %3D

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Q: Examine the continuity of if 0 a at

A: We need to examine the continuity of the given function f(x) at x=a.

Q: Prove that the function g:R → R* • defined by g(x) = 2* is an injective homomorphism that is not…

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Q: 2. Let f: R → R_be f(x) = 1+ |r|" (a) Is f everywhere defined? If not, give the domain. (b) Is f…

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Q: Let f map C2 into C2 be a linear operator such that for every x in C2, f(f(x)) = x. Let V+ = {x in…

A: Let f:C2→C2 be a linear operator such that for every x∈C2, ffx=x.  Suppose V+=x∈C2:fx=x and…

Q: Let f : R + R defined by f(x1, x2)) = x1 - 2. Then determine if is (a) Lipschitz continuous(if it…

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Q: Let f: R/{1} → R given by f(x) ==, for every x € R/{1}. Then the given f is %3D x-1 bijective.

A: Topic:- function

Q: . Let R be the relation on N defined by xR y if x and y share a common factor other than 1.…

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Q: Use Green's Theorem to evaluate F dr, where F(2, y) = (9xy, y" - 8) and C is the rectangle with…

A: That's easy. Have a great day!!!

Q: Let f be a mapping from [1,+*[ to [1. +[ defined by f(x) = x+1/x. Then f has a unique fixed point O…

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Q: Let f(x,y) = x - 5xy -y². Compute f(6,0), f(6, – 2), and f(b,c).

A: Solved below

Equations and Inequations

Equations and inequalities describe the relationship between two mathematical expressions.

Linear Functions

A linear function can just be a constant, or it can be the constant multiplied with the variable like x or y. If the variables are of the form, x2, x1/2 or y2 it is not linear. The exponent over the variables should always be 1.