Let A = {1,2,...,n} and consider the functions f: A → A. a. How many functions satisfy f(1) = 1? b. How many functions satisfy f(1) # 1 or f(2) # 2? c. Of the functions f: A → A with f(1) = 2 and f(2)=3, how many are bijections?

Q: a. Find all functions from {0, 1} to {1}.b. Find two relations from {0, 1} to {1} that are not…

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Q: a. Find all functions from {0, 1} to {1}. b. Find two relations from {0, 1} to {1} that are not…

A: We have the domain is A=0,1 and the range is B=1 First we find the relations from A=0,1 to B=1: The…

Q: a. Let X = {2, 4, 6} and Y = {a, b, c, d'}. Define g : X→ Y by the following arrow diagram. X 2 4 bo…

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Q: Refer to the following functions: p(x) = x2 + 2x – 15 x +1 9(x) x-3 r(x) = v7-x Which of the…

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Q: let f be the function x²-C for x< 5 flx)=3x+5c for X Z 5

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Q: Let g be the function g(x)=x²-x. Find g(-a). O None of these. O-a² + a O a² +1 O-a²-a O a² + a O…

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Q: {(1, c), (2, a), (3, d)}, a function from X = {1,2, 3} to Y = 5. Given g {a, b, c, d}, and f =…

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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: Which of the following relation is a function? a) S = {(1,–2),(–3,6), (-3,2), (-1,6) b) T = {(-2,3),…

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Q: Let f : N x N H R be defined by (a + 1)(a + 2b) f (a, b) = (a) Show that the image of f is contained…

A: given that                                           f:N×N→R is defined.…

Q: Use a formula to express w as a function of t if w - V4s + 5 and s- ef - 1.

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Q: . Determine if y is a function of x in x = y? + 5.

A: Given equation - x = y2+5Let's solve for y =- y2 = x-5y = x-5       ........(1)

Q: Let X = { n Î Z | 1 £ n £6 } and consider the two functions f : X ® X , g : X ® X , expressed in…

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Q: Given that A = {1, 2, 3, 4, 5} and B = {x, y, z}, determine which of the sets of ordered pairs…

A: 1.  i) This ordered pair doesn't represents a function because the values 'y' corresponding to x= 4…

Q: Consider the set N²= NX N, the set of all ordered pairs (a, b) where a and b are natural numbers.…

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Q: Given x = {5,10,15,20,25,30} and y function from X to Y. Let f(5) = 400, f(10) = 100, f(15) = 500, f…

A: x=5, 10, 15, 20, 25, 30  &amp;  y=100, 200, 300, 400, 500, 600. f5=400,  f10=100,  f15=500,…

Q: Lêt X {2, 4, 6} and = {a, D, C, a}. Define g:X→ by the following arrow diagram. X Y a 2 4 C 6. d The…

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Q: f'(t) = tf(t). HINT: Write f'(t) – tf(t) = 0 and multiply the equation by e-2/12.

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Q: 4. Let m and b be real numbers, and consider the following three functions: f(x) = 2x + 1, g(x) = -x…

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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…

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Q: what sets X and Y is the function X Y defined by 3x f (x) = x +4 %3D ijection?

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Q: ƒ(x) = = ax² + 3x + b 9x² - 6x + 2a if x ≤ 0, if x > 0.

A: f(x)={ax2+3x+b if x≤09x2−bx+2a if x&gt;0