Show that a one-one function                 f : {1, 2, 3} → {1, 2, 3} must be onto.

Q: A of A is a function from A to A that is both one-to-one and onto.

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Q: Determine whether or not the function f : Z × (Z − {0}) → Z is onto, if f((m, n)) = ⌊m/n ⌋. (Use…

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Q: 1. Let f : Z6 → Z6 be such that f(7) = x2 + 3. (a) Is f a well defined function? (b) Is f…

A: Since you have posted a question with multiple sub-parts, we will solve first three sub parts for…

Q: Suppose f: A g(b)= {a E A | f(a) =b}. Prove that if f is onto then g is one-to-one. What if f is not…

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Q: Suppose that f and g are functions, and that they are left inverses of each other. Prove that f og…

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Q: Theorem 4. Let X be a set, and let F: X Y be a l-1 and onto function. (a) F-lo F = Idx (b) FoF- =…

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Q: Let A={a,b,c,d,e}. Find a relation R on A which is symmetric and transitive but not reflexive

A: Reflexive relation means every term of a set is related with itself

Q: Let f: X → Y and define x~y if f (x) = f (y). Show that - is an equivalence relation on X.

A: The objective is to show that ~ is an equivalence relation on X.

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: Let f : {1, 2, 3} → {a, b, c} be one-one and onto function given by f(1) = a,   f(2) = b and f(3) =…

A: Consider

Q: Let Z be the set of integers and f:Z Z be defined as f(x)=-2x-3. Then the inverse function of exists…

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Q: Let f, g,h: A→ A be any bijective functions. Then (f ogoh)-

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Q: Let f :A→B and g : B +C be functions. Show that if g o f is onto, then g is onto.

A: Given: f:A→B and g:B→C are functions Given: gof: A→C is onto To show: g:B→C is onto That is,  for…

Q: يثبت The Cauchy-Schwarz inequality states that (f, g)| ≤ ||f||||g|| for every f, g ¤ H.

A: Using the property of inner product

Q: 5. Determine whether the function f : Z × Z →Z is onto if a) f (m, n) = m² + n² b)f (m, n) = m³

A: See the solution.

Q: Exercise 2.12. Determine whether or not the given functions f:Z Z are one-to-one or onto (or neither…

A: The solution of given functions is given as follows :

Q: Let f be the function from {a, b, c, d} to {1, 2, 3} defined by f(a) = 3, f(b) = 2, f(c) = 1, and…

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Q: (a) Prove that there exists a function f : Z → Z so that f is one-to-one but f is not onto. (b)…

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Q: Prove that a function f: AB is surjective if and only if it has the following property: for every…

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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 X = {1,2,3,4} and Y = {5,6,7}. State whether a function f: X → Y can be one-to-one or not…

A: By using definition of one-time and onto function we solve the given problem :

Q: Is the function f(x) = x + 1 from the set of integers to the set of integers onto?

A: For onto from set A to B, Every value of set B should exist atleast once in the function.

Q: Let f be the function from {a, b, c, d} to {1, 2, 3, 4} with f(a) = 4, f(b) = 2, f(c) = 1, and f(d)…

A: For bijection, the function needs to be one to one and onto.

Q: 1- DETERMINE A AND BEC FOR THAT THE FUNCTION: (f:C+a=+b -2 +az +b f(=) = IF = #1-i, 2-1+i (f(1– i)…

A: Continuity of complex function:

Q: Give an example of(a) a function f : Z → N that is both one-to-one and onto N; and(b) a function f :…

A: Here, we need to give an example of(a) a function f: Z → N that is both one-to-one and onto N.

Q: Show that a map f : X → Y invertible if and only if f is one-to-one and onto

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Q: Suppose f: A→ B and g: B→ C are functions, show that a) If both f and g are one-to-one, then go f is…

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Q: Let f : Z → Z be relation defined by f(x) = ||æ| – 5|+ x for all æ E Z. i) f is a function ii) f is…

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Q: A function is bijective if it is both 1-1 and onto. Prove that the function below is not bijective…

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Q: Let X = {1,2,3,4} and Y = {5,6,7}. State whether a function f : X → Y can be one-to-one or not…

A: By using definition of one-time and onto function we solve the given problem :

Q: 7. If a functionf defined in [a, b] is such that o (i) f is derivable in [a, b], (ii) f' (a) and f'…

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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: Let g: A ---------- B andf: B-----------C. Prove that f is onto if f 0 g is onto.

A: Given:g:A→B;     f:B→CTo Check : if (f∘g):A→C then f is ontoNow given…

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: (a) Prove that there exists a function f: Z → Z so that f is one-to-one but f is not onto. (b) Prove…

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Q: 1. Give an example of a function that is one-to-one but not onto. Give an example of a function that…

A: An example of a function that is one to one but not onto b) an function that is not one to one but…

Q: Is the function f(x) = x2 from the set of integers to the set of integers onto?

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Q: Which of the following function f: Z XZ → Z is not onto? f(a, b) = a O f(a, b) = |b| f(a, b) = a - b…

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Q: Let f : A → B and g : B –→ C be functions. (a) Prove that if gof is one-to-one, then f is…

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Q: Let function f:Z Z be defined as follows; x– 1 x is odd f(x) = < (x² + 2 x is even The function f is…

A: Let, x=2 that is x is even. Then, fx=x2+2 So, f2=22+2=6f-2=-22+2=6 Therefore, f2=f-2 Then, the given…

Q: Prove that f is an onto function. Is f an invertible function? If so, find the inverse function of…

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Q: A function f :N Z which is one-to-one and onto.

A: Suppose we have a function . Condition of f is one-one . Suppose such that , then . Condition…

Q: (a) Prove that there exists a function f : Z→ Z so that f is one-to-one but f is not onto. (b) Prove…

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Q: Which of the following function f: R X R → R is not onto?   1 2x - 3   2 3x3 - x   3 x2-2x…

A: The first function is fx=2x-3 which is linear and hence onto The second function is fx=3x3-x solve…

Q: Let f: {4,5,6} → {1,2,3} be a function defined by f(x) = x-3. Prove that f is injective and…

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