For two sets A = {a, b, c}, B = {7,12, 13, 17, 30} fis a injective function from Ato B If f (a) = 1ănd f (b) = 30what is the sum of all possible values of f (c}

Q: Give the domain of the function. z = 4x – 5y O {(x, y): x and y are real and 4x – 5y = 0} O {(x, y):…

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Q: if and only if F-1: R(F) →X is bounded.

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Q: 2. Let X be a set, and let A C X. Define a function f: P(X)→ P(X) by f(B) = AUB for all BE P(X).…

A: Given: 2) Here the given is im(f) = f(A)  A ∈ P(X) = C∈P(X)  A ⊆C, We have to show that im(f) =…

Q: Generate the graph of f(x) = x + 2x + 3 with a graphing utility, and use the graph to find a number…

A: Here to find δ, we can use the epsilon delta definition of continuity which states that: f(x) is…

Q: Let A and B be two sets with |A| = n and |B|| = m, where n and m are positive integers. Answer each…

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Q: Evaluate the sum of with x1 = 0, x2= 2, x3 = 4, x4 = 6, and Ax= 1, for f(x) = 5x -2. i=1 4. i=1

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Q: If f(x, y) = 2√x² + y² - 16, then the domain of f is the set D = {(x, y)]x² + y² ≥ 4}. Select one:…

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Q: 8. Let X and Y be sets, and let C and D be any two sets of Y, and suppose that F: X →Y is a…

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Q: Let A and B be two sets with |A|| = n and |B|| m, where n and m are positive integers. Answer each…

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Q: 7. Let A = fa; b; c; dg and B = fx; yg. (a) How many functions are there from A to B? How many of…

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Q: Find a function f(k) such that 5 +7+9+11+ 13 = . Σ k=0 f(k) =

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Q: 6. If X and Y are finite sets, prove that |X'| = XY, Here, XY is the set of all functions from Y to…

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

Q: Suppose that p(x) = {24 + x, if x< 2) | 1+x², if x 2 2 Find a value of A such that the function p(x)…

A: Given query is to find the value of A.

Q: For each of the functions f1, f2, f3, determine whether it is injective, surjective, and/or…

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Q: For the function f: (0, 1) → R, f (x) = 2"x+ {2"x}, (n, m e N; n > m), the number of points of…

A: Let's find.

Q: a. If f(x,y) is convex with respect to (x,y) and C is a convex set, show that g(x) = infyec f(x,y)…

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Q: The domain of the function f(x,y)= V1-x²-y² +In(x²+y² – 1) is empty Select one: O True O False

A: we have to find the domain for f(x)

Q: * The domain and range of the function y= In (x- 1) are.50 All x greater than 2 and All y O All x…

A: We have to find

Q: Iff: X→ Y is a function and F is a nonempty family of subsets of y, then o(ƒ˜¹ (F¹)) =ƒ˜¹ (0 (F)).

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Q: Suppose that the functionss and t are defined for all real numbers x as follows. s (x) = x t (x) =…

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Q: (5) Let ƒ : A → B and g : B → C, where f and g are functions and A, B, and C are sets. (a) Prove…

A: In 2 nd part construct a function

Q: Give the domain of the function. q = VP1 + 4p2 O {(P1, P2): P1 and p2 are real and p1 + 0} O {(P1,…

A: In this question we have to find the domain of the function.

Q: Can you help me with this?

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Q: Which of the following is a requirement of p(x) but not a requirement of f(x)? has to be less than…

A: We have to find f(x)

Q: If f(x, y) = 2√√x² + y2 - 16, then the domain of f is the set D = {(x, y) x² + y² ≤ 16}. Select one:…

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Q: d) Let XCR be a set and f: X→ X be a function. If X is compact and convex, then f admits a fixed…

A: d) If X is compact subset of R then X is closed and bounded. If X  is convex subset of R then X is…

Q: If f A —> B and g : B —> C are injective function, then gof: A —> C is an injective function. Prove…

A: Given that f: A→B is given injective. this implies cardinality of set A is less then cardinality of…

Q: Evaluate the sum of f(x) Ax, with x, = 0, x2 = 2, X3 = 4, X4 = 6 i=1

A: Given,     ∑i=14f(xi)∆x=?Where    x1=0, x2=2, x3=4, x4=6, and ∆x=2,            f(x)=3x-1

Q: If f(x, y) = 2√/16 - x² - y², then the domain of f is the set D = {(x,y)|x² + y² ≤ 16}. Select one:…

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Q: F C 11. From the following ultimate class frequencies of the positive and negative classes and the…

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Q: Find the least integer n such that f (x) is O(x") for following function. f(x) = 17x +10x³

A: Given function is fx=17x4+10x3 We have to find the least integer n such that fx is Oxn. Since, the…

Q: Q1. (a) How many functions are there from a set with 3 elements to a set with 5 elements?

A: We find total number of functions from a set with 3 elements to a set with 5 elements.

Q: what is the range of h if the domain of h is a set of negative integers?

A: Given: h(x)=[x]+2

Q: Consider f : {1, 2, 3} → {a, b, c} given by f(1) = a, f(2) = b and f(3) = c. Findf-1 and show that…

A: Given function is

Q: If h is defined by  h(x) = |X| + 2, What is the range of h if the domain of h is the interval…

A: The given function is h(x)=x+2

Q: For a function f(x) = peª + qe¬ª where p and q are non-negative real numbers such that p + q = 1,…

A: Provided function is: f(x)= pex+qe-x , p and q are non-negative real numbers and p+q=1 q=1-p. Value…

Q: A number-theoretic function f is said to be multiplicative if f(m,n) = f(m)f(n): :Select one O For…

A: Introduction: When the domain of a function is the set of positive integers or more precisely the…

Q: Give the domain of the function. q = VP1 + 5P2 O {(P1, P2): P1 and p2 are real} O {(P1, P2): P1 and…

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Q: Let (x, Y, z) = In (z - vx² + y? ). (a) Evaluate f(3, -4, 8). In(s - V3? + (-4)² ) (b) Find the…

A: we know domain of ln(x) is set all x for which x&gt;0.

Q: 2. If f : A → B and g : B→ C are injective functions, then gof: A → C is also injective.

A: We need to prove/disprove statenemt two.

Q: Prove that for any sets C,D⊆Y and for any function f:X⟶Y, f−1(C∩D)=f−1(C)∩f−1(D).

A: We will prove the given statement.

Q: (c) The domain of the relation Z is the set of all real numbers. xZy if y = 2x

A: The relation Z is the set of all real numbers. xZy if y=2x. Z=x,y|y=2x (a)The relation R on set A is…

Q: If f(x, y) = 2√16- x² - y², then the domain of f is the set D {(x, y) x² + y² ≤ 16}. Select one: O…

A: Given - fx,y=216-x2-y2 To determine whether the set D= x,y|x2+y2≤16 is the domain set of f or not.

Q: Represent graphically the set of values of z for which 3 < 2 2 + 3

A: According to the given information, it is required to represent the given function graphically.

Q: If the function f:R → R given by f(x) =x³+ax²+bx+5sin*is an increeasing function , Find the…

A: if F(x) is increasing function, then F'(x) must be greater than 0. So from that, we will solve this…

Q: (b) The domain of the relation A is the set of all real numbers. XAy if |x-y| <2

A: b. To check the reflexive, for any x∈ℝ then, x-x=0≤2 That is, for all x∈ℝ, xAx. Therefore, A is…

Q: The domain of the relation A is the set of all real numbers. Ay if |x-y| ≤ 2

A: Given relation is A=(x,y): x-y≤2, x,y∈ℝ Here x is the domain of the relation.

Q: Find the sum of the values of f(x) = x³ over the integers 1, 2, 3, ..., 10.

A: The given function is fx=x3, over the integers 1,2,3.......,10.

Q: Q: A- find for the functions: - In =) + In(3x2) = In(3) %3!

A: