Let f and g be the function from the set of integers to itself, defined by f(x) = 2x + 1 and g(x) = x ^2. The composition of fog (-2) is
Q: Consider the function f:Z→Z defined by f(x)=3x? - 1. Find f-(10), f"(13), Let f:R -> R be defined by…
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Q: Consider for what value of x are the following function defined? а) f(x) 3 Зх — 2 - b) f(x) = 1 %3D…
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Q: f(x) is O(g(x)) if and only if g(x) is Ω(f(x)).
A: Proof: given: f:R---->R g:R----->R f(x) is O(g(x)) so we can say |f(x)|≤c|g(x)|.........(1)…
Q: Question 11 For all a and b in the domain of a function f, the function is injective iff…
A: Injective is basically a one on one function. No two elements can map to the same domain. So if a=b…
Q: Let A = {1, 2, 3, 4} and B = {a, b, c}. Give an example of a function f: A -> B that is neither…
A: A = {1, 2, 3, 4} and B = {a, b, c} f: A -> B
Q: make a 3 variable k map with the function: xy(bar)z+x(bar)yz+xz
A: The given expression can also be written as: - Also, the expression is in the SOP form, but SOP…
Q: More asymptotic notation. Let f, g, h : N → R2º. Prove or disprove that if f +gE O(h), then f E O(h)…
A: The solution for the above given question is given below:
Q: F(X,Y,Z)=(22÷7)(0,2,5,7)
A: F(X,Y,Z)=(22÷7)(0,2,5,7) = π(0, 2, 5, 7) Hence, this boolean function is in POS(product of sum)…
Q: The mapping f: R → R, f(x) = x2, which of the following are correct? f is one-to-one. f is not a…
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Q: Give an explicit formula for a function from the set of all integers to the set of positive integers…
A: given: explicit formula for a function from the set of all integers tothe set of positive integers…
Q: Define upper bound. If f(n) = 3n * 5 for what values of C and n this function is said to be upper…
A: The answer is provided below.
Q: 10. Simplify the following function using Karnaugh maps: F(A,B,C,D) =E(3,7,11,13,14,15) Final…
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Q: For all a and b in the domain of a function f, the function is injective iff f(a) #f(b) → a=b…
A: I have given an answer in step 2.
Q: Determine whether the function f(x) = 4x−1 where f:R→R is a bijection. If it is not, explain why…
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Q: Given the function H = A'B'C+ A'BC'+ A’BC+ ABC'+ ABC A. What are the minterms and maxterms…
A: The function H contain terms and their equivalent minterm is A'B'C = 001 = 1 A'BC' = 010 = 2 A'BC =…
Q: H.W2 Minimize the following function using K-Maps: F (A, B, C, D) = Σ m (1, 5, 6, 12, 13, 14) + d…
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Q: A={a,b,c,d,e} and let b the set of letters in the alphabet. Let the functions f,g,h from A to B be…
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Q: Given f1(x) = −3x + 4 and f2(x) = x2 are functions from R to R. Find: a. f1.f2(x) b. f1.f2(-1)
A: Answer: The solutions of both the parts are given below-
Q: Let f and g be the function from the set of integers to itself, defined by f(x) = 2x + *1 and g(x) =…
A: Answer: fog(x) = 6x+9
Q: 5. Simplify the following functions using a K-map: h)F(W,X,Y,Z)=X'Y'Z'+XYZ'+WXY+W'X'Y'+WZ
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Q: justify whether each of the following functions is injective, surjective, bijective, or none of…
A: following function is surjective
Q: Define a function f: Z* to Z* by the rule: for each integer n, f(n) = the sum of the positive…
A: Answer : Below mentioned screenshot explains the answer of both question.
Q: how many functions a) map {1,2,3.4.5.6} to {up,down,left,right} b) how many functions in part a…
A: Solution:
Q: 4, By constructing two function f and g, f,g: (0, 1] → R such that f is injec- tive and g is…
A: The solution for the above given question is given below:
Q: * .Determine whether the function f: Z × Z →Z is onto if f (m, n) = m + n onto one to one not one to…
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Q: 3. Use B-reductions to evaluate the following lambda term to a normal form. (\f x->f (f x)) (\n f…
A: I attaced your answer in below.
Q: Let i, j ∈ Za and w, x ∈ Zb with i, j different from each other and w, x different from each other.…
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Q: Reduce the following function using k-map technique, F(A, B, C, D) = π(0, 2, 3, 8, 9, 12, 13, 15).
A: The Answer is in Below Steps
Q: countability of the set of functions that map positive integers to {0,1}
A: In the question we have to find weather the set is countable or uncountable.
Q: Determine whether or not the function f : Z × Z ! Z is onto, if f((m, n)) =m-n.
A: Determine whether or not the function f : Z × Z ! Z is onto, if f((m, n)) =m-n.
Q: Draw a Karnaugh map for the following function; X= [m(0, 2, 3, 6, 7, 8, 10, 11, 14, 15) Then…
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Q: Let S and T be sets with: |S| = 5, |T| = 7 %3D How many one-to-one functions are there from S to T?…
A: There are D. 7!/2 one-to-one functions from S to T.
Q: Question 7 The function f(x)=x2 from set of positive real numbers to positive real numbers is not…
A: The function f(x)=x² from set of positive real numbers to positive real numbers is________ not…
Q: Given set A={1,2,3,4}, B={1,2,3,4), and the mapping f: A → B, where f={(1,1), (1,2), (2,1), (3,3),…
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Q: 1. Create a K-map for each of the following functions: i. X1 X2| f 0 0| 1 1 1 1 1 ii. f (x1, x2, x3)…
A: K-map:- Without using any Boolean algebra theorems, we can easily minimize Boolean expressions of…
Q: A Pythagorean triplet is a set of three natural numbers, a b c, for which, a^2 + b^2 = c^2 For…
A: Before we procced further let us do some fundamental maths! let a = m2 - n2 b = 2*m*n c = m2 +…
Q: Let f and g be the function from the set of integers to itself, defined by f(x) = 2x + 1 and g(x) =…
A: EXPLANATION: Composition of function is basically the application of one kind of function to the…
Q: F(x, y, z) = xyz + xy’z’ + x’yz + x’y’z
A: Let the user assume the variables x,y,z as A,B,C respectively Then the expression becomes F(A,B,C)=…
Q: Q2) Simplify the following function for F using a K-map. F(A,B,C,D) = E m(0, 2, 8, 10, 12, 14)
A: solution of the given function is-
Q: 4x+1 A function fis defined on the det of real numbers by f(x) = 2x-3 i) Write down the domain of f.…
A: Complete answer is given below .
Q: Simplify the following functions using a K-map: d)F(X,Y,Z)=m0+m2+
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Q: 4. Represent the following function as a list of maxterms and use a k-map to find the minimal…
A: Here in this question we have given a function with some min term and. We have asked to use kmap to…
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A: It is defined as a powerful general-purpose programming language. It is used in web development,…
Q: ample, a > b contains such an operator that compares th
A: Solution - In the given question, we have to fill the correct answer.
Q: 5) Write the maxterm function F1 = M1.M2, M3.M5.M7 and simplify it. (Without using Karnaugh Map)
A: Introduction of Maxterms and Minterms: In digital logic, the output of any function is either 0 or 1…
Q: Let f be a function from the set of length 10 binary numbers to the set of subsets of A={1, 2,…
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Q: Give an explicit formula for a function from the set of integers to the set of positive integers…
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Q: Select the property(ies) of the given function f:Z→Zf(x)=9x+1 O fis a bijection f is one-to-one None…
A: The properties for the given function is as follows.
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- Given g = {(1,c),(2,a),(3,d)}, a function from X = {1,2,3} to Y = {a,b,c,d}, and f = {(a,r),(b,p),(c,δ),(d,r)}, a function from Y to Z = {p, β, r, δ}, write f o g as a set of ordered pairs.Give an explicit formula for a function from the set of all integers tothe set of positive integers that is onto but is not one-to-one.A = {0, 1, 2, 3, 4} B = {2, 3, 4, 5}Given the sets A and B, how many constants maps are there from A into B.
- Show that if f(x) and g(x) are functions from the set of real numbers to the set of real numbers, then f(x) is O(g(x)) if and only if g(x) is Ω(f(x)).Let f be a function from the set of length 10 binary numbers to the set of subsets of A={1, 2, ...,10 } given by f(b1,b2...b10)={i in A|bi=1}. Determine f^-1({1,3,5,6})For this question, you will be required to use the binary search to find the root of some function f(x)f(x) on the domain x∈[a,b]x∈[a,b] by continuously bisecting the domain. In our case, the root of the function can be defined as the x-values where the function will return 0, i.e. f(x)=0f(x)=0 For example, for the function: f(x)=sin2(x)x2−2f(x)=sin2(x)x2−2 on the domain [0,2][0,2], the root can be found at x≈1.43x≈1.43 Constraints Stopping criteria: ∣∣f(root)∣∣<0.0001|f(root)|<0.0001 or you reach a maximum of 1000 iterations. Round your answer to two decimal places. Function specifications Argument(s): f (function) →→ mathematical expression in the form of a lambda function. domain (tuple) →→ the domain of the function given a set of two integers. MAX (int) →→ the maximum number of iterations that will be performed by the function. Return: root (float) →→ return the root (rounded to two decimals) of the given function. START FUNCTION def binary_search(f,domain, MAX =…
- For this question, you will be required to use the binary search to find the root of some function f(x)f(x) on the domain x∈[a,b]x∈[a,b] by continuously bisecting the domain. In our case, the root of the function can be defined as the x-values where the function will return 0, i.e. f(x)=0f(x)=0 For example, for the function: f(x)=sin2(x)x2−2f(x)=sin2(x)x2−2 on the domain [0,2][0,2], the root can be found at x≈1.43x≈1.43 Constraints Stopping criteria: ∣∣f(root)∣∣<0.0001|f(root)|<0.0001 or you reach a maximum of 1000 iterations. Round your answer to two decimal places. Function specifications Argument(s): f (function) →→ mathematical expression in the form of a lambda function. domain (tuple) →→ the domain of the function given a set of two integers. MAX (int) →→ the maximum number of iterations that will be performed by the function. Return: root (float) →→ return the root (rounded to two decimals) of the given function. START FUNCTION def binary_search(f,domain, MAX =…How do we define that a function f(n) has an upper bound g(n), i.e., f(n) ∈ O(g(n))?Consider the following functions mapping Real numbers to Real numbers. For each of the following pair of functions determine both its both g o f as well as its f o g. f(x) = 6x3; g(x) = 2x f(x) = (x-1)/2; g(x) = 4x2
- Consider the function f : N × N → N given byf(m, n) = 2m-1(2n − 1), (m, n) ∈ N × NShow that f is bijectiveWrite a function linear_independence that takes a collection of vectors with integer entries (each written as a list), and returns True if this collection of vectors is linearly independent, and False otherwise. Examples: linear_independence([1,2]) should return True. linear_independence([1,3,7],[2,8,3],[7,8,1]) should returnTrue. linear_independence([1,3,7],[2,8,3],[7,8,1],[1,2,3]) should return False.how many functions a) map {1,2,3.4.5.6} to {up,down,left,right} b) how many functions in part a are subjective? c) how many have f- inverse(up) =2