Let f and g be functions from {1,2,3,4} to {a,b,c,d} and from {a,b,c,d} to {1,2,3,4}, respectively, with f(1)=d,f(2)=c, f(3)= a , and f(4)=b, and g(a)= 2,g(b)=1,g(c)= 3 , and g(d)= 2. a. Is fone to one? Is g one to one? %3D Is fonto? Is a onto?

Q: Find two functions f and g such that h (x) = (f • g)(x). h (x) = |3 – 2x"| Select a function forf…

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Q: The function f : {0, 1}² → {0, 1}³ is defined as: For every x E {0, 1}², ƒ(x) = 0x Select the set…

A: Since f(x)=0x. Thus the range of f is 0(domain).

Q: Let f(0) = 3 and 2 ≤ f′(x) ≤ 4 for all x in the interval [−5, 5]. Determine the greatest and least…

A: Using mean value theorem we get: For some x between 0 and 2

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

A: If f(a) = c  then f-1(c) = a.

Q: Find the domain of the function. h) - 5) X - A) {x|x 0}, or (0, -) B) {x|x 1), or (-, 1) u (1, ) D)…

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Q: Let f(x) = 3x + 1, x, = -1, x, = 0, x3 = 1, x4 = 2, and X5 = 3. Find E f(x,).

A: we have the given the following details   f(x)=3x+1x1=-1x2=0x3=1x4=2x5=3We have to find∑i=15f(xi)

Q: 5. (a) Let f: S T be a function, and A CT and BCT be subsets. Show that (A-B) = f-1(A) - f-(B). ww

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Q: Let f, and f2 be two functions from R to R such that f, (x) = x4 and f2 (x) = x - 5. What are the…

A: Given data f1 and f2 are two functions from R to R  and  f1 = x4 , f2 = x - 5

Q: Find the composition of functions, if it exists. f = {(-4, 1), (-2, 4), (0, 5), (2, 6), (4, 8)} g =…

A: f={(-4,1),(-2,4),(0,5),(2,6),(4,8)}g={(-1,-3),(0,2),(1,4),(2,5),(3,7)}h={(-3,-5),(-1,-1),(1,1),(3,5)…

Q: 4. Describe the domain of the function f(x, y)= In(6+ x-y). {(x, y): y<x-6} {(x, y): y 2 0} {(x, y):…

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Q: Find f + g, f - g, fg, and f/g and their domains. f(x) = x,       g(x) = √x

A: Hello. Since your question has multiple sub-parts, we will solve first three sub-parts for you. If…

Q: In Rolle's theorem .If f(x) be a real valued function in (a, b] such that f(x) is continuous ir A.…

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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: A table of the function values for f(x) and f'(x), and a graph of the piecewise linear Function g(x)…

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A: In this question, we need to determine whether there exists any function for the given conditions.

Q: The domain of a functionf of the two variables x and y is a subset of R.

A: Given statement  The domain of a function f of two variables x and y is a subset of R.

Q: 5. Determine the end behavior of the function y= -x(x+2)(x- 5)- В. As x→ -00, y - → o and as x A As…

A: To determine the end behaviour of the function

Q: y is a function of x, which of the following cannot be true?   A. When x = 3 and x = 7, then y = 2.…

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

A: given: we have to determine the value of the composite function:

Q: 3. Iff and g are two lincar functions: f(x)-axtb and g(x)- cx+d, then what are the conditions on…

A: Disclaimer: Since you have asked multiple questions, we will solve the first question for you. If…

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

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Q: Let g be a piecewise-defined function given by: 7x + Vx² + 5 2х- 4 if x 3

A: Find the values at which the peicewise function g(x) is undefined.

Q: What is the end behavior of the given function? f (x) = 3V-x – 2 As x → 0, f(x) → -∞. As x → -, f(x)…

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Q: Let h(x) = f(x)*g(x), and k(x) = f(x)/g(x). g(x) has points (-2,-1), (-1,-2), (1,0), and (3,2). f(x)…

A: see below the answer

Q: 2 Suppose y is a function of x such that y * and y(4) = -3. Find y. |

A: The differential equation is given by y' = 2x                                   .......(1) Initial…

Q: Let f be the function {(1,4),(2,1),(3,3),(4,2)} and g be the function…

A: Composition of Functions: If and , then the composition of f and g dented by is defined by Note…

Q: If f(x, y) = A In (x² - y) -x+y+1 O {(x, y) x² > y, {(x,y)|x² ≥ y, ○ ○ {(x, y) x² > y, | then the…

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Q: Given f(x) and g(x) = x – 7 () Determine the domain of: O (-0,0) U (0, 2) U (2, 7) U (7, ∞0) O (-00,…

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Q: the function f, evaluate f(−6), f(−5), f(−1), and f(0). f(x) =    x + 4   if   x < −5 −2x − 1   if…

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Q: 2. If f(x) is an even function and g(x) is odd function, then a) f(x) g(x) is an function. b) f(x)…

A: Solution:-

Q: What is a 1–1 function? A function f is a 1–1 function if, for any a and b in the range of f, f(a) =…

A: Given:[1]. A function f is a 1–1 function if, for any a and b in the range of f, f(a) = f(b) implies…

Q: If two functions are defined as: g: from (1,2,3} to {a,b,c}, and g(3) = a, g(2) = b, g(1) = c h:…

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Q: a real valued function in [a, b] such that f(x) is different in A. (a, b) B. [a,b C. (a,b] D. [a, b)

A: In Rolle's theorem, if f is real-valued in [a,b] then, f is differentiable in,  (a,b)   The correct…

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: Prove that if f(x) and g(x) are both even functions, then h(x) = f(x) + g(x) is an even function.

A: Given that f(x) and g(x) are both even functions.  That means: f(-x)=f(x) and g(-x)=g(x) [by…

Q: Find the domain of the function. if x 6 O(-0, 0) U (0, 2] U (6, 0) O(-0, 0) U [2, ∞) O(-∞, 2) U [6,…

A: The domain of a function is the set of input or argument for which the function is real and defined.…

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

A: Given: Three functions, f: {1, 2, 3, 4} → {a, b, c, d} f(1)= d f(2)= b f(3)= a f(4)= c g: {a, b, c,…

Q: If g' (x) = Ofor all values of x in the interval (a, b), then g is a constant function. True False

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Q: Exercise 2. Let f : A → B be a function with Y1 and Y2 subsets of B. Prove that if Y1 C Y2, then…

A: Let f:A→B be a function and let Y1,Y2⊆B. Suppose that Y1⊆Y2 To show f-1(Y1)⊆f-1(Y2) Let x∈f-1(Y1)…

Q: Let g : Z x Z -→ Z x Z be the function given by g(x, y) = (3x + y, x – y). Find, with proof, an…

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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: Let f(x, y) : = x/Y Evaluate f(3, 4)

A: We need to evaluate f(3,4) To evaluate we need to plug in 3 for x  and 4 for y

Q: If Q is a function of w, x, y, and z, each of which is a function of r, s, and t, how many dependent…

A: It is given that  Q is function of w, x, y and z it means that the value of Q depends on the…

Q: b. Determine whether each of these functions from {a, b, c, d} to itself is one-to-one. i. f(a) = b,…

A: We are entitled to solve only one question at a time so, I am providing you the answer of first…

Q: Let S = {a, b, c, d}, and let f1: S → S, f2: S → S and || f3: S → S be the following functions: fi =…

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Q: Find functions f and g so that h(x) = (f • g)(x). h(x) = 2 %3D x-2 f(x) = 1/x, g(x) = x²-2 f(x) =…

A: Given: hx=fogx and hx=1x2-2 hx=fogx=fgx  So, fgx=1x2-2 Check fgx for each given option (i) fx=1x,…

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

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Q: Function f:Z+ Z, defined by f(n) = n – 1 is a one-to-one function. True False

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Q: If f(x) and g(x) are defined on domains A and B, respectively, then the domain of f(x) + g(x) is…

A: here given that domain of f(x) and g(x) are A and B then we will find the domain of f(x)+g(x) that…

Q: Let f = {(1,1), (2,3), (0,–1), (–1, –3)} be a function from Z to Z defined byf(x) = ax + b, for some…

A: