Question 2(a) Are the following functions surjective? Justify your answers.(i) The function a : Z → Z defined by a(n) = 3n + 1.(ii) The function b: Zx Z→ Z defined by b(m, n) = 3m + n.(iii) The function c: N→ N defined by c(n) = the number of digits of n².(b) Let f: Z→ Z be defined by f(n) = 3n+2. Find a function g: Z → Z such that g of is theidentity function on Z.(c) Is g an inverse for f? Justify your answer.

Answered: Image /qna-images/answer/856b9347-7bfc-4271-8bb8-992a8b72f27d.jpg

Answered: (a) Are the following functions…

Advanced Engineering Mathematics

10th Edition

ISBN:9780470458365

Author:Erwin Kreyszig

Publisher:Erwin Kreyszig

Chapter2: Second-order Linear Odes

Section: Chapter Questions

Problem 1RQ

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The transformation of a function f(x) into a function g(x) is given by g(x) = Af(Bx + H) + K. where the constants • A vertically scales the function. (negative A reflects the function about the x-axis.) • B horizontally scales the function. (negative B reflects the function about the y-axis.) • H horizontally shifts the function. K vertically shifts the function. Transform f(x) into g(x) where the transformation is g(x) = f(-) The function f(x) is shown below in red. Graph the transformed function g(x) by first placing a dot at each end point of the new transformed function and then click on the "line segment" button and connect the two blue dots. (Hint: Use pattern-matching to determine the values of the constants A, B, H, and K.) 4- -6 -5 -4 -3-2 -1 4 -2 -4 -5
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The transformation of a function f(x) into a function g(x) is given by g(x) = Aƒ(Bx + H) + K. where the constants • A vertically scales the function. (negative A reflects the function about the x-axis.) • B horizontally scales the function. (negative B reflects the function about the y-axis.) • H horizontally shifts the function. • K vertically shifts the function. Transform f(x) into g(x) where the transformation is g(æ) = f(x - 3) The function f(x) is shown below in red. Graph the transformed function g(x) by first placing a dot at each end point of the new transformed function and then click on the "line segment" button and connect the two blue dots. (Hint: Use pattern-matching to determine the values of the constants A, B, H, and K.) 6+ 4 -6 -5 -4 -3 -2 -1 1 2 3 4 5 -2 -3 -4 -5-
f(x + h) – f(X) h#0. for the function f(x) = /x- 11. [Hint: Rationalize the numerator.] Find the difference quotient of f; that is find The difference quotient of f; f(x) = Vx- 11 is. (Simplify your answer.)
Suppose that in a certain biology lab experiment, the number of bacteria is related to the temperature 7 of the environment by the function N(T) = -27² + 250T - 4900 (40 ≤ T ≤ 90). Here, N(T) represents the number of bacteria present when the temperature is T °F. Also, suppose that t hr after the experiment begins, the temperature is given by T(t) = 10t + 40 (0 ≤ t ≤ 5). (a) Compute N[T(t)]. N[T(t)] = (b) How many bacteria are present when t = 0 hr? When t = 2 hr? When t = 5 hr? t = 0 hr bacteria bacteria t = 2 hr t = 5 hr bacteria
The function f(x) = 8x – x² is increasing on : A. (-00, 4). B. [4,0). C. [0, 8]. D. [-8, 0]. Select one: O A O D O B O C
For the function f(x)equals 4 x squared minus 21 x minus 18 , a. Calculate the discriminant. b. Determine whether there are 0, 1, or 2 real solutions to f(x)equals 0. a. The discriminant is nothing . (Simplify your answer.)
The transformation of a function f(x) into a function g(x) is given by g(x) = Af(Bx + H)+K. where the constants • A vertically scales the function. (negative A reflects the function about the x-axis.) • B horizontally scales the function. (negative B reflects the function about the y-axis.) • H horizontally shifts the function. • K vertically shifts the function. Transform f(x) into g(x) where the transformation is 9(х) — — 2- f(а+ 3) + 3 The function f(x) is shown below in red. Graph the transformed function g(x) by first placing a dot at each end point of the new transformed function and then click on the "line segment" button and connect the two blue dots. (Hint: Transform the function by applying the constants in this order: H, B, A, K.) 6+ 4 -6 -5 -4 -3 -2 -1 2 3 4 5 -2 -3 -4 -5 -6+ Clear All Draw: Dot Line Segment
|2. Given f(x) = -x² + x – 5, find and fully simplify f(x+ h).
The transformation of a function f(x) into a function g(x) is given by g(x) = Af(Bx + H)+ K. where the constants • A vertically scales the function. (negative A reflects the function about the x-axis.) • B horizontally scales the function. (negative B reflects the function about the y-axis.) • H horizontally shifts the function. • K vertically shifts the function. Transform f(x) into g(x) where the transformation is g(x) : = 3· f(x) The function f (x) is shown below in red. Graph the transformed function g(x) by first placing a dot at each end point of the new transformed function and then click on the "line segment" button and connect the two blue dots. (Hint: Use pattern-matching to determine the values of the constants A, B, H, and K.) 구 4 -7 -6 -5 -4 -3 -2 -1 1 2 3 4 5 6 7 -2- -3- -4- -5- -6- -7- Clear All Draw: Dot Line Segment Question Help:
2. Consider the function y(x) = 5x over the interval [0, 10]. (a) If the points A(0, y(0)), B(5, y(5)), and C(10, y(10)) are on the curve represented by the above function, find the slope of the lines (secants) AB, and AC, respectively. (b) If x represents time and y represents the displacement of a particle moving along a line, what is the physical meaning of your results to part (a)? (c) Now consider a point D(10 – h, y(10 – h)) on the curve represented by the given function, find the slope of the line DC. (d) As h → 0, what is the limiting value of your result to part (c)? (e) What is its physical meaning of your result to part (d) if again x represents time and y represents the displacement?
The function P(r) = – 3.75x? + 775x – 7500 gives the profit when z units of a certain product are sold. Find a) the profit when 85 units are sold dollars b) the average profit per unit when 85 units are sold dollars per unit c) the rate that profit is changing when exactly 85 units are sold dollars per unit d) the rate that profit changes on average when the number of units sold rises from 85 to 170. dollars per unit e) The number of units sold when profit stops increasing and starts decreasing. (Round to the nearest whole number if necessary.) units

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