9. Determine whether f is injective, surjective or bijective. a. Suppose f: N→ N has the rule f(n) = 4n + 1. b. Suppose f: Z → Z has the rule f(n) = 3n² – 1. c. Suppose f:Z-Z has the rule f(n)-3n-1. d. Suppose f : N →→ N has the rule f(n) = 4n² + 1. e. Suppose f: R → R where f(x) = [x/2].

Q: 4. Find g[h(x)] if g(x) = x² and h(x) = x + 3. %3D O A. x2-- 3 B. x + 6x +9 O C. x + 3x? O D. z + a…

A:

Q: Which of the following functions are increasing? Decreasing? A. y= 3x + 2 B. Y= -5x-9 C.y 7 D. y =…

A: ANSWER:

Q: What is the end behavior of f(x) = 2 O a As x→∞, x) → -3. As x→∞, fx) → ∞0. As x→∞, f(x) → -3. As…

A:

Q: 5. Let X be the set of odd integers and Y = {a € Z | a is even and a ≤ 20}, and consider the…

A: (a) Let, f(x) = f(y)          => x(9 – x) = y(9 – y)          => 9x - 9y - x2 + y2 = 0…

Q: Exercise 1. Suppose t₁ (n) = O(n²) and t₂(n) = O(n²). Encircle in the following list all the…

A:

Q: 14. Let X = {n eN:0 < n < 999} be the set of all numbers with three or fewer digits. Define the…

A: A

Q: 3. Suppose that f and g are functions with the rules f(x) = 4x - 7 and g(z) = r. Find (f o g)(x) =…

A: The given function is fx=4x-7 and gx=x2

Q: K9. What is the end behaviour of f(x) (x + 5) (2 - x)(x − 4)? - - x →∞, y → ∞; x ⇒ − ∞, y →∞ Ox→∞, y…

A: Given: fx=x+52-xx-4 To find: End behaviour of f(x) First simplify the given function to find the end…

Q: 8. A function g : Z → Z is defined by g(n) = 3n – 2. Let D be the set of odd integers. (a) Determine…

A: The objective is to solve the above question.

Q: The Maclaurin series for f(x) = x'e2) ts: -2)*x**2 (b) (a) (e) None kl k!

A:

Q: 15.K. Let f be monotone increașing on / [а, б] to R. If c € (a, 6), dehne l(c) l(c) = sup {f(x): I…

A:

Q: #8: Suppose that an = as 8n a₁²2² +2a₂x³ + 3a3x²4 + 4a4x³ + ... (i) Σf(n)x"+2 n=0 (ii) g(n)x+1 We…

A: This is a good exercise in summation and we shall see how to change the indices.

Q: 4. Use the definition of "f(x) is 0(g(x))" to show that 2* + 17 is O(3*).

A:

Q: O D. 2x + 2x+4 Find f(-x) when f(x) = 2x-2x+4. OA. O A. 2 +2x-4 O B. -2x +2x +4 OC. -2x + 2x-4 O O O

A:

Q: Determine b so that f(x) is continuous if O 8 x + 6 xS 6 f( x ) = D O 2 x2 + bx +10 x > 6 b =

A:

Q: (1) Let f be a function from A to B, {An} a sequence of subsets of A, and {B} a sequence of subsets…

A:

Q: 5. Which of the has a domain of (-0, +o)? a. f(x) =x b. f(x) = x? c. fx) =x d. f(x) =x* 6. Given the…

A: Use the basic property of function and composition of function.

Q: Given f(x) = x +9 and g(x) =-x-7, find (f-g)(x). O A. x- x+2 O B. x + x + 16

A: Explanation and Solution is given below....

Q: Suppose f and g are two functions with nonnegative values. If f(n) is (n) and g(n) is (n³/2), then…

A: We have given that , f and g are two functions with non - negative values. If fn is θn. Also , gn is…

Q: 6. Let f and g be two arithmetic functions with g(n) = Σan f(d). If g is multiplicative, then so is…

A:

Q: 3. Let f : R → R and g : R → R be defined by f(x) = 3x + 5 and g(x) = x² + 7. Find the composition…

A:

Q: 4. Let f(x) = g(x) = x -5, k-(10) +7 = 10 and h (x) = find: ther b. Domain of h(x). c. (hof)(2). (Z…

A: (NOTE:   As nothing is mentioned, so all functions are taken as real valued functions.)

Q: Let A = {1, 2, 3}, B= {4,5,6, 7} If f: A x B → N with f((a, b) = b – a , find the following. a. f…

A:

Q: 3. For f(x) = 15x²-3 16x²+9x+8 As x → ∞, y → || As x →∞, y →

A:

Q: 7. For each of the following, give an example of functions f: A → B and g: B C that satisfy the…

A:

Q: - Determine the behavior off(x) = (x-1)(x+2)' x → 1- f (x) →_ x → 1+ f(x) →. x → -2- f(x) → x → -2+…

A:

Q: mplete the following statements. x) is positive when g'(x) is decreasing x) is negative when…

A:

Q: Determine whether -2, if z < -2 *, if - 22122 |8- z), if 2<z <3 |4 -r, if z 23 f(a) = is continuous…

A: givenf(a)=-2, ifx&lt;-2x5 , if-2≤x≤28-x , if2&lt;x&lt;34-x2 , ifx≥3one limit of this piecewise…

Q: 1. If x[n] is given below, sketch the functions listed. a. x[n+4] b. x[3-n] c. x[n]u[n] d.…

A:

Q: Q1. Let f,g : R → R be given by f(x) = 6x – 10 and g(x) = 4x+5. Find the domain of f(x) h(x) =…

A: Given             f(x)=6x-10           g(x)=4x+5            h(x)=f(x)fog(x)…

Q: 4. (a) Let a : Z→ Z be the function defined by a(n) = 2n + 1, and let i: Z → Z be the identity…

A: