Let A = B = {1, 2, 3}, and consider the function f: A → B defined as follows: f(1) = 3, f(2) = 1, f(3) = 3.       f is onto only     f is one-to-one only     f is one-to-one correspondence        f is neither one-to-one nor onto

Q: Question (2): Let f,g: R R = R- 0 be any continuous functions. are they homotopic?

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Q: QUESTION 4 set S = {1,2,3}, set T = {10,20,30}, set V = {a function g: S T function h: T V h(10) =…

A: Introduction: A composite function is the composition of two different functions. For example,…

Q: QUESTION 18 Determine if the function defined below is one-to-one, onto, both, or neither. f:X Y…

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

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Q: Suppose h is a function such that h(1) = -2, h'(1) = 2, h"(1) = 3; h(1) =-2, h(2) = 6, h'(2)= 5,…

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Q: QUESTION 3 Determine if the function defined below is one-to-one, onto, both, or neither. 1. 2. 3.…

A: Here, note that the domain of the function is 1,2,3,4,5 and the range{a,b,c,d,e} is

Q: A relation F : A → B is a function if and only if Va E A. O |F(a)| = 1 O |F(a)| > 1 O |F(a)| > 1…

A: First option is true by definition only.

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Q: Question 17 Consider f : X →Y, with domain X = {l, z, h, d, n, p, u, e, v, j, s,t} and codomain Y…

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Q: Question 6: a) Let O be the set of odd numbers and O' (1, 5, 9, 13, 17, ..) be its subset. Define…

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Q: QUESTION 7 Let f: Q Z be defined by f(r) (the ceiling function). Is f (a) onto? (b) one to one?

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Q: Question 18 Consider f : X →Y,with domain {c, g, 0, e, d, p, 2, U, M, s, n, v} and codomain Y = {69,…

A: 18. Given is a function f from X to Y where, X = {c, g, o, e, d, p, z, u, m, s, n, v}, Y = {69, 10,…

Q: Let A= [1,2] U [3,4] and f: A-→Rbe defined by f(x)=Dx when x E [1,2] and f(x)=Dx-1 when x E [3,4],…

A: f(x)=x, 1≤x≤2x-1, 3≤x≤4

Q: Theorem 12. Let f be a non-zero continuous function on R such that f(x+y)=f(x) f(y) ¥x, yER. Show…

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Q: Theorem 7.11 (Pasting lemma). Let X = A U B, where A, B are open in X. Let f : A → Y and g : B → Y…

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Q: 5. Given a function f: A → B. Define the relation f from P(A) to P(B) by f = {(X,Y)C P(A) × P(B) | Y…

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Q: Question 9 Given f: RR and f(x) = x, then O All of the given choices are true. O f(x) is one-to-one…

A: The objective is to find the correct option.

Q: let a = (-1 - 1) and b= (t u v w). define a functionn F: a TO B BY FOLLOWINNG ARROW DIAGRAM

A: let a = (-1 - 1) and b= (t u v w). define a functionn F: a TO B BY FOLLOWINNG ARROW DIAGRAM

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A: Please see below picture for detailed solution.

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Q: Let E = {n E Z|n is even} and let O = {n E Z|n is odd}. Define a function f: E × O + Z by f(x, y) =…

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Q: QUESTION 7 Match the following properties of the function with their definitions. Function f is a…

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Q: If m, n ∈ N, then (f^m)^n = f^(mn).

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Q: Let g: [-2,2] → R be defined as follows: if - 2<x<0 1 g(x) = if x = 0. %3D if 0<x<2 Then there…

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Q: QUESTION 19 Define a relation S from R to R by (x, y) ES, if and only if x² + 3y² = 25 %3D (a) List…

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Q: (a) Let X = {1,2,3,4} and Y = {a,b,c}. Define H :X→Y as follows: Н(1) — с, Н(2) %3 а, Н(3) — с, Н(4)…

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Q: -B- Let f( M,(Z).+.)-(M,(Z),+..) be a function define by such that g( v: al e M,(Z) . Is f is…

A: The given question is epimorphism. Given that,      f : M2ℤ , + , · → M2ℤ , + , · is a function…

Q: Question 4 ($2 Q10] Determine whether the following relation is a function from R into R. Also…

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Q: Question 4 Let f: M M be a uniformly continu- ous function. Which of the following is false? (A) If…

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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: Question 3. Given the function f : R → R defined by if x 1 f(x) = 21² +x-1 r+1 a. Find the image…

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