(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 N.(c) Is g an inverse for f? Justify your answer.

Answered: Image /qna-images/answer/9517431c-6255-4171-b5d5-ac618477dba6.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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3. Let f (x) = 2x2 – 4. Find the indicated function values. - (a) f(3) (b) f(0) (c) f(-5) (d) f(6b) (e) f(b + 2)
2. State why the function f(z) = 2z² - 3 - ze² +e-² is entire.
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
The domain of the function f(t) = t-3 is (-v2, v2) and [3,00] t2-2
8. Given the functions f(x) = 2x +5 and g(x) = x² – 4, find (f + g)x. а. 2x? + 5x? - 8х - 20 b. 2x - 5x? – 8x – 20 c. 2x + 5x² + 8x – 20 d. 2x + 5x² – 8x + 20 9. Given the functions f (x) = 2x +5 and g(x) = x² – 4, find (4) x. 2x+5 a. 10. Given the functions f(x) = 3x² + 2x² + x + 1 and g(x) = 2x² – 1, find (S – 9)x. a. 3x² +x b. 3x +x+2 c. 3x² + 2x² + x d. 3x + 4x? +x +2 11. Evaluate the lim a. +0 b. -00 c. d. Indeterminate
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:
The transformation of a function f(x) into a function g(a) is given by g(a) = 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(z) where the transformation is g(a) = f(# – 1) + 3 The function f(E) is shown below in red. Graph the transformed function g(z) 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.) 2 -6 -5 -4 -3 -2 -1 1 2 3 4 5 6 -2 -3 -4 -5 Clear All Draw: Dot Line Segment Check Answer
2. State why the function f(z) = 2z² - 3-ze² +e-² is entire.

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