where f: Z+ --> Q+ (a) prove or disprove: f(n) is one-to-one (b) prove or disprove: f(n) is onto (c) does f have an inverse? why or why not? discrete mathematics

Q: Let f(x) =(x-1)(x-2)(x-3),Prove that there is more than one "c" in (1,3) such that f'(x) =0

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Q: Verify that the three conditions of the Rolle Theorem hypothesis hold for the function f (x) = 1-2x…

A: Three conditions of the Rolle's theorem hypothesis. Consider function f(x), it should be continuous…

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

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Q: Prove f-1(E U F) = f-\(E) U f-1(F)

A: We have to prove that f−1E∪F=f−1E∪f−1F. Let x∈f−1E∪F hence, x∈f−1E∪F⇔fx∈E∪F…

Q: Consider the function f : R → R such that f(x) = -5x –- 7. 1. Prove that f is a one-to-one function.…

A: The solution is given as

Q: There exists a function f such that f(x) > 0, f(x) 0 for all x. True False

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Q: Let f (x) and g(x) be defined by f(x) = 2 - x      g(x) = (x2 + 2x+ 2    x < -1…

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Q: 6. (a) Use the Schröder-Bernstein Theorem to prove that [a, b]| = |(a,b)| for any a, b e R. (b) Use…

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Q: consider the function f(n) = where f: Z+ --> Q+ (a) prove or disprove: f(n) is one-to-one (b) prove…

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Q: Using intermediate value theorem, the function f(x) = x* – 9 has a root over O 12,3[ O 10,1[ O 1,2[…

A: We use the Intermediate Value Theorem to answer the question.

Q: f:R- {- } - 5x-4 -, f(x) = %3D 3x+7

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Q: Function: Let f:Z>Z be such that f(x)=x+1. What is the inverse of f(x) b. Let f:Z>Z* be such that…

A: (a)

Q: Let X_1 and X_2 be sets. Define functions  pi_1: X_1 x X_2 -> X_1, pi_2:X_1 x X_2 -> X_2 by…

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Q: Let f be an arithmetic function f with f(1) ‡0. Then there exists a unique Dirichlet inverse f-1 of…

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Q: Consider the function f : R → R such that f(x) = –5x – 7. 1. Prove that f is a one-to-one function.…

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Q: 5. Let f (z) be analytic in some domain. Show that f (z) is necessarily a constant if either the…

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Q: 1. Prove that if f is multiplicative, then E lu(d)\f(d) = II(1+ f(p)). Suggestion: Modify the proof…

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Q: 2. Let f be continuous and differentiable everywhere. Suppose that f(-1) = f(1). Show that there are…

A: Here, we will apply Rolle's theorem which is stated as: Let f be continuous on [a, b], a &lt; b, and…

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Q: f (a) a theorem with direct proof (b) a theorem with indirect proof

A: this is a question of mathematical logic.

Q: 1. Define function f : Z+ → Z such that f(n) = /n. (a) Is f one-to-one? Justify (prove) your answer.

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Q: Let R denote the set of real numbers. Let f: Rx R-> R x R be a bijective function defined by f(x, y)…

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A: (a) Suppose g o f is 1-1. To prove f is 1-1.

Q: Prove that -(x+y)=(-x)+(-y).

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Q: Define (i) "f(x) is 0(g(x))", (ii) "f(x) is N(g(x))" and (ii) "f(x) is O(g(x))" Using the definition…

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Q: 6. Prove that there does not exist a multiplicative function f such that f(30) = 0, f(105) = 1, and…

A: We have to prove the given statement.

Q: Using intermediate value theorem, the function f(x) =x² – 0.5 has a root over O 1-1,0[ O 12,31 O…

A: the intermediate value theorem states that if f is a continuous function whose domain contains the…

Q: Domain of F Co-domain of F X Y F a • d• Domain of G Co-domain of G X Y G a • b e of d• a. Is F…

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Q: Let f be an arithmetic function f with f(1) #0. Then there exists a unique Dirichlet inverse f-1 of…

A: Definition: (Arithmetic function) A function f:ℕ→ℂ is called arithmetic function. Definition:…

Q: atation for f(r) = In(5- a) and %3D

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Q: Prove that function f: Z x Z -> Z x Z defined by formula: f(m, n) = (4m + 3n, 3m +2n) is bijective.…

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Q: 3- i) Let f: A→B and g: B-C. If gof is one to one (1-1), then show that f is one to one. ii) Let h:R…

A: Injective Function.

Q: 2. Let f be continuous and differentiable everywhere. Suppose that f(-1) = f(1). Show that there are…

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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: (A) Verify if the function f(x)= x² +5x+6 satisfies criteria stated in Rolle's theorem on |-3, 2 and…

A: f(x)=x2+5x+6 in the interval -3,2

Q: Let f : R → R be an increasing function. Show that f(x) = x, ∀x ∈ R ⇔ f(x) = x, ∀x ∈ Q.

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Q: 4. Let Z be the set of integers and f : ZxZ - ZxZ be a function defined by f(х, у) %3D (х,х — у)…

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Q: 6. Based on what you know about the multiplicative principle, how many functions f:A- Bare there if…

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Q: true or false? PROVE YOUR ANSWER b) If f :N→N and g :N→N are functions such that f is not onto but…

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Q: 4. Let f : R+ x Z → R+ be the function defined by f (x,n) = x", where R+ is the set of positive real…

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Q: Advanced Calculus) Determine whether f (t) is at least piecewise continuous in the interval [0, 10].

A: Given that: f(t)=2t   ,  0≤t&lt;20     ,   2≤t≤10     NOTE: As per our answering guidelines, we can…

Q: Exercise 1. Let R be the set of real numbers and f: R-(0}→R-{1} be the bijective function defined by…

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Q: (*;)-()0)

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Q: Q1.Let f be the function from R to R with f(x)=x^2.Is f invertible?

A: f(x)=x2 , ia function from R to R. This f is not invertible because it is not onto function i.e…

Q: Definition 6. A function f : A → B is an injection (or is one-to-one) if and only if whenever x # y…

A: A function f:A→B is said to be an injective if and only if whenever x≠y, then fx≠fy To rewrite the…

Q: g) Prove that f : R → R where f(x) = x² – x is not injective. h) Disprove the following claim by…

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