7. Decide which of the following functions are (a) one-one, (b) onto, (c) both, (d) neither. (a) f : Z x Z → Z defined by f(n, m) =n – m. (b) g : Z x Z Z × Z defined by f(n, m) = (n, m). (c) h: Z Z × Z defined by h(n) = (4n + 5, 3).

Q: 25. For the function f(x) = 45x3 - 3x5, determine the interval(s) for which f(x) decreases. O (3, 3)…

A: We will solve this question by  differentiating f(x) and then finding the intervals for which the…

Q: Let f(z) = 4r- 12x +7 then f(r) is decreasing on Select one: O a (-00, -1), [12, o0) Ob [1,0) O…

A:

Q: 3. Find the largest domain (in R2) for the function In(3 + y) 1- x + y f (x, y) :

A: Let's find.

Q: 10. A function f(x) has domain {x ɛ R} and range (y ɛ R, y 2 2}. What would be the domain and range…

A: The domain of f is the range of f-1 and the range of f is the domain of f-1. Here domain of f(x) is…

Q: I have the following example:  "For the function f : A = {a, b, c, d, e} → B = {1, 2,..., 6}…

A:

Q: 7. Let f : (0, 20] → R be given by f(x) = x² – x – 2, and let g : [1, 50] → R be given by 1 g(x) 1…

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Q: – 2ay + i(bx -

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Q: Suppose f(x, y, z) = xyz + 2xy + 2² · Compute the following values -(2,8₁16) - (-2,-8, 16) (1,-1,0)…

A: We have to find functional value.

Q: Consider these functions. 1) Evaluate (f + g)(2). f(x) = 3x² – 5 g(x) = Vx - 2 A) -1 B) 0 C) 3 D) 7…

A: we have the given functions  f(x)=3x2-5 g(x)=x-2 1) (f+g)(2)=f(2)+g(2)…

Q: f(x+h)-f(x) 2. Evaluate h If a. G) f(Vx) b.

A:

Q: 3. Determine whether each of these functions from is one-to-one/onto. (a) f : R → R, f(x) = 3r. (b)…

A: A function f is one-to-one if every element of the range of g corresponds to exactly one element of…

Q: x+7, -4 h er. f(0) = 7. f(1) = 8, f(2) = -5, and f(3) = -10, of b

A:

Q: In(2 - a) x² + y² – 16' Determine the domain of the function f(x, y)

A: The domain of a function is the values of the variables of the function that result in a defined…

Q: 12. Let f be the function f(x)={ x² - 3bx+2; x2 For what value of b is f continuous at x = 2 ? (A) 0…

A: To find For what values of b is f is continuous at x=2.

Q: 4. Let f-(x) = g(x) = x-5, k-1(10) + 7 = 10 and h(x) = then find: b. Domain of h(x). c. (hof)(2). (Z…

A:

Q: Fxy(x, y) is a monotonic and non-decreasing function of both x and y.

A:

Q: If f(x) = v(x - 1)/ (x - 9), then the domain of f is given by the interval A. (1, +00) B. (-3, +3)…

A: The given function is  f(x) = sqrt[(x - 1)/(x2-9)]

Q: 4. Let function f: R → R and function g: R → R be two functions for which f(g(x)) = x and g(f(x)) =…

A: We have to prove given statement.

Q: Suppose f: (0,00) → (0, ∞) and g: (0, ∞o) → (0, ∞o) are continuous functions. True or false: If g…

A:

Q: 1. Let N = {1, 2, 3,...} and let f: N→ N be a function given by f(x) = 2x + 3. (i) Find f(f(4) + 1).…

A:

Q: 3. State the domain and range of f(x) = –- 2 D:(-x,0] А. D: В. D:[-2,0) C. D:[1,0) D. R:(-0,-1]…

A: To state the domain and range of,fx=-12-x-1

Q: Suppose that F(x) is a function such that F"(x) = f(x). Which of the following statements is true? […

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: Determine where the function f(x) = O A. (-∞, ∞) 1-00 O B. O C. O D. 3 3 3 (-∞0,²21) U ( 212,00) N/W…

A: we have to find out the values of x where function is continuous.

Q: (a) Are the following functions surjective? Justify your answers. (i) The function a : Z→ Z defined…

A:

Q: Write the formulas of fog for pairs of real functions f, g. (a) f(r) = x², 9(x) = x – 2 (b) f(x) =1,…

A: A composite function is generally a function that is written inside another function. Composition…

Q: 2 Suppose y is a function of x such that y * and y(4) = -3. Find y. |

A: The differential equation is given by y' = 2x                                   .......(1) Initial…

Q: 2. Let f: RR by f(x) = -2x + 1. Let A = [2,5] B = [-1,3] C = [−2,3] D = [1, 4]. Find each of the…

A: Here are the solutions:  Note:We have provided the best possible solution for you. Kindly, verify…

Q: 3. (a) If f: X→ Y and g: Y→ Z are functions and go f is one-to-one, must f be one-to- one? Why/Why…

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: Let f, g and h be R- R functions, f(x) = 2x - 1, g(x) = 3x+1, and h(x) = x +1. Compute the following…

A: I will solve all three subparts for you and provide detailed answers.