7. Q7; Functions (a) Prove that the function f : Z4 → Z12 given by f(T) = [3x] is wel defined. x+1 (b) Let f(x) and g(x) = x2 + 1. %3D x + 2' i. Find fog, gof. What are the domains and ranges of these functions? ii. Determine if f and g are one to one or onto. iii. Determine if fog or g of are one to one or onto.

Q: Find the domain of the function. Then compute the value of the function at the given point. f(x,…

A: To calculate domain of f(x,y)

Q: 10. Consider the function f (x) = x³ + 6x2 -36x + 4. Then I. f decreases on (-6, 2) and increases on…

A:

Q: 4. Consider the function Check whether f is concave, convex or neither. f(x, y) = x² - y² + 2xy + 2x…

A: Please find attachment for the details solution

Q: Which relation is not a function? a. N (y) = Vx b. N (y) = ±Vx c. N (y) = -Vx d. N (y) = vx – 1

A: A relation is a function if there is exactly one output for every input.  means for every x value…

Q: 6.3 Let g: R → R be a real-valued function defined by g(x) = x² + 2x - 1. Let A = (-2,3], and B =…

A:

Q: Use the graph of the function f shown to the right to find f(-1), f(0), and f(1). f(-1) =

A: Given the graph of function of f . To find f(-1) , f(0) and f(1) using the graph.

Q: The function f (x) is a line segment that has endpoints P 3) and 1. Determine what f (x) is. 2. Find…

A: Given query is to find the the function of the line from the coordinates.

Q: 1. Given that f is the function defined by f(x, y) = 2¹+y²-²-2y, determine the relative extrema of f…

A:

Q: Consider the function f whose graph is drawn below. For which values of x is the function…

A:

Q: Let P(s) be the function - 1. Find the following: | s+1 P(7) = %3D P(- 9) = %3D P() - %3D 8. In each…

A: Since, you have posted question with multiparts. As per guidelines we"ll solve only first three…

Q: 2. Check the following function f(z) = iz – 3z is analytic or not (Use C.R equations).

A:

Q: Let f: R2 R2 be the function given by f(x, y) = (x + y, y). Prove or →>> 8. disprove: f is…

A: Function which is one to one

Q: Let f(r) = 2. 1 + Find f(1/2) 1. Find the domain of f ii.

A: Given data is: fx=11-21+11-x Calculate the value of f12 and the domain of the function.

Q: What are the local extreme values of the function f(x) = a – 6x? + 2? a. None of these. O b. Local…

A: Extreme vlue of the function, using second derivative test

Q: (e) 2= /-(x + y)². (f) z -(x² + y² + 3). (g) z = 1 - ม

A:

Q: If f(z) = u+iv is an analytics function.where u and v are conjugate function. Given one of these say…

A:

Q: Let f(x) = (4x – 6)(x² – 5). Find all the values of x for which f'(x) = 0. Present your answer as a…

A: Given fx=4x-6x2-5

Q: Determine a potential function to evaluate (F*dR for C any path from the first point to the second.…

A: Given:F=3x2(y2−4y)i^+(2x3y−4x3)j^​Two points: (x1, y1) = (-1, 1)(x2, y2) = (2, 3)To determine a…

Q: III. Verify if the function is continous at the point. 1. f(x) = x³ – 2x² + x – 5 at x = 0

A: f(x) is continuous at x=0 if- limx→0-f(x)=limx→0+f(x)=f(0)

Q: Evaluate the function. 2. Find h(3,6) when h(x,y) = 3x +y J3x+y O A. 9 O B. 10 O C. 3/5 O D. 5/3

A: We have given function  hx,y = 3x+y2 Put x = 3 , y = 6 h3,6 = 3×3+62 h3,6 = 9+36 h3,6 = 45 h3,6 = 35

Q: 6. Which of the following function lal are NOT linear function? L y= 7x -1 IL. y- m. y = 6 IM. y-…

A:

Q: 1. Given f(x) is a one-to-one function with Df: [4,25] U (42,100] and Rf: (-o,-14], find the domain…

A:

Linear Algebra

In mathematics, problems can be solved by the arithmetic operators like addition, subtraction, multiplication, and division. In algebra, we represent the numbers by any letter called a variable. If these variables are of degree 1, then it is studied under linear algebra. The first-degree equations involving algebraic expressions are called linear equations. That is, if you represent it by drawing a graph you will get a straight line.