3. Let the function f :R → R be defined as follows:(3х-1if x>3f (x)={x² – 2 if - 2

Given f(x) = 3x-1ifx>3x2-2if-2≤x≤32x+3ifx<-2

Answered: 3. Let the function f :R →Rbe defined…

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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Let f(x, y) 1 1 - x² - y² domain of f is the set D = {(x, y)|x² + y² > 1}. Select one: True O False then the
A. B. f(x) f(x) 1 -3 9. 3 4 1 4 6. 7 2 4 С. D. f(x) f(x) 3 -1 3 3 3 3 4 4 3 5 3 3 7 Which table does NOT represent a function? A) A B) C) D) 2101 6. 6 O23
4) i) Let f: N→ C be a function with f(30) = 0, f(70) = 1 and f(105) = 1. Determine whether f is multiplicative or not. Explain why. Show that f(1) = 0 or f(1) = 1 if f is multiplicative. Determine whether the following functions are multiplicative or not. Give a detailed ii) iii) explanation. a) f(n)= ^ 1 if n 1 mod (2) 2 if n2 mod (2) b) f(n) = 1 if n 1 2 if n2 3 if n 0 mod (3) mod (3) mod (3)
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= mx + b. 4. Let m and b be real numbers, and consider the following three functions: f(x) = 2x + 1, g(x) x + 2, and h(x) A. If function f has a codomain of (5, 7) U (7, 9), the largest its domain can be chosen is (2, 3) U (3, 4). Explain. B. If function g has a codomain of (−1, 1) U (1, 3), the largest its domain can be chosen is (-3, 3) U (3, 9). Explain. C. Within the context of the e- definition of a limit, your result from part A suggests that if € is equal to 2, the largest that can be chosen for function f(x) is 1. Explain. =
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3. Let the function f :R →Rbe defined as follows: [3x–1 if x> 3 f (x)={x² – 2 if -2