What is an antiderivative? A it is the reverse process of differentiation. it is an integer that can be expressed as a product (ratio) of two integers, a, where the integer a is called B the numerator and the integer b is called the denominator and where b * 0. it is a group or collection of objects that are called members or elements of the set. it is the infinite process of differentiation.

Q: In Section 1.2 we showed that ordered pairs can be defined in terms of sets and we defined Cartesian…

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Q: Prove or disprove: composition of functions is commutative; that is g◦f = f ◦ g when both sides are…

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Q: Examine each of the following relations given below and state in eachcase, giving reasons whether it…

A: (i) R = {(2,1),(3,1), (4,2)} For one value of x, we got one value of y So it is a function.…

Q: Explain the Wronskian of 2 functions f and g ?

A: Let f and g are the two functions. The Wronskian of the n functions is the determinant of the matrix…

Q: How do you show the inverse image of the intersecction of S and T equals the intersection of the…

A: To prove : f-1(S∩T)=f-1(S)∩f-1(T) To show f-1(S∩T)=f-1(S)∩f-1(T) need to prove…

Q: (d) Operator -iħd/dx and function exp(-ikx). (e) Operator -ħ?d?/dx² and function exp(-ikx).

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Q: Consider the following function: | 4x 9z -19 1 -1 -9z 19 f(2) = 3 13 0 0 0 a) What is the highest…

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Q: Write out all functions f: {1,2} {a, b, c, d) (in two-line notation). How many functions are there?…

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Q: Explain 'For two given sets A and B, not all relation are function'. Show an example

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Q: 10. Explain the concept and notation of a function space

A: In mathematics, a function space is a set of functions of a given kind from a set X to a set Y. It…

Q: Let A = {1, 2, 3}, B = {4, 5, 6, 7} and let f = {(1, 4), (2, 5), (3, 6)} be a functionfrom A to B.…

A: givenA = {1, 2, 3}, B = {4, 5, 6, 7} and let f = {(1, 4), (2, 5), (3, 6)} be a functionfrom A to B

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

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Q: How do you show the image of the intersecction of S and T is a subset of the intersection of the…

A: Let function f from A into B. Let S and T are subset of A. To show that fA∩B⊂fA∩fB. Let y∈fA∩B. To…

Q: Example 10 Let X = {a, b} and Y = {1,2,3}. Find the number n of functions: a. From X into Y, and b.…

A: Suppose, set X has p elements and set Y has q elements. Then, the total number of functions from set…

Q: Does the following set represent a function? R = { (0,0), (1, -1), (1,1), (3,-1), (3,3) } What is…

A: Here we use the concept of functions.

Q: 2. Describe the transformations that map the base function y = 2* , onto the - 3(2**) - 3 given…

A: We will describe the transformation.

Q: Find the function U, whose first difference is *C,-

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Q: For what values of p is the set of ordered pairs {(1,3), (2p, 4),(4,p)} a one-to-one function? A p…

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Q: 3. Let A = {1, 2, 3, 4}. Let F be the set of all functions from A to A. (a) How many pairs (f, g) E…

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Q: Evaluate the function at the specified points in the figure below

A: A function is a relation which maps each value in its domain to exactly one value in its range. The…

Q: Examine each of the following relations given below and state in each case, giving reasons whether…

A: (i) Since 4, 5, 6 are the elements of domain of R having their unique images, this relation R is a…

Q: Let A = {x, y} and B = {w,z}. Describe all relations from A to B. Indicate which of these are…

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Q: Exer. 57-58: (a) Find the domain and range of the function. (b) Find the inverse of the function and…

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Q: 3 2 -1 -4 +2 -1 1 4 6. -1- -2 -3 -4

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Q: 3. Let A = {1,2, 3, 4}. Let F be the set of all functions from A to A. (a) How many pairs (f, 9) €Fx…

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Q: and let B = {1,2,3,4}. Provide examples injective surjective injective but not surjective surjective…

A: A function  is said to be injective if , for . That means every distinct element of the domain is…

Q: How do you show the image of the union of S and T is equal to the union of the image of S and the…

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Q: 3. List all distinct functions from the set A = {1,2} to the set B = {a,b}. How many such distinct…

A: Solution -Given that  A={1,2}  and  B={a,b} Then number of distinct functions from A to…

Q: Define Function spaces.

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Q: Determine whether the function f from {a, b, c, d} to {1, 2, 3, 4, 5} with f (a) = 4, f (b) = 5, f…

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Q: 3. Iff= {(-7, 1), (-5, 8), (3, 11), (5, -1)} and g = {(-6, 4), (-5, 3), (-1, 7), (5,5)}, what is f +…

A: Given that, f={(-7, 1), (-5, 8), (3, 11), (5, -1)} and g={(-6, 4), (-5, 3), (-1, 7), (5, 5)}