Given the table below determine whether y is a function of x and if the fuction is a one to one X: 4,0,3,9,2 Y:-2,13,9,0,2

Q: Let f : R → R be a function with the following property: |f (a) – f(b)| < 4|a – b| for all a, b E R.

A:

Q: Find f(a), f(a + h), and the difference quotient for the function given below, where h = 0. f (x) =…

A: The given function is f(x)=4x-3

Q: Consider the functions: f(x) = a², g(x) = x – 1, h(x) = Va, k(x) = - and m(x) = x + 1. %3D Write…

A: I am going to solve the given problem by using the simple algebra to get the required result.

Q: A contour map for a function f is shown. Estimate the value of fy(1, 5) 20 200 15 160 120 10 80 40 3…

A: Note: Hi! Thank you for the question as per the honour code, we’ll answer the first question since…

Q: A contour map for a function f is shown. Estimate the value of fy(1, 7) 30 400 320 20 240 10 160 80…

A: To estimate fy(x,y) use the slope of a secant line in the y direction

Q: determine which statement is true {(x, y)|x = y2} (A) not a function (B) function; domain: R (C)…

A:

Q: Assuming f and g are differentiable functions, determine ) (2) if f(2) = 5, f' (2) = –7, g(2) = 8,…

A:

Q: determine if the relation defines y as a function of x

A: A relation is a function if there exists a unique output or y-value for each input or x-value. In…

Q: Select all of the following tables which represent y as a function of æ and are one-to-one. 5 8 8 3…

A: A function f(x) is one to one if no two elements in the domain of f(x) correspond to the same…

Q: Let C be the contour (blue) given in the figure below and let f(z) be any function with If(2| < 2/2.…

A: third option is correct

Q: Let f: XY and A,BCX. Give an example of a function f and sets A and B that f[A\B] #f[A]\f[B]

A: Take any constant function and subsets A and B such that they overlap.

Q: Which of these two relations are functions? Select the two that apply: 1 3. 4. 4. 6. 13 ty 12 y -2…

A: To check whether the relation is function or not, By definition of a function, The function is a…

Q: Consider the function f (x) = In arrow notation, which of 2-x-6 the following describes the behavior…

A: Simplify the function and calculate the limit

Q: Assuming f and g are differentiable functions, determine (f/g)'(4) if f(4) = 5, f'(4) = -7, g(4) =…

A:

Q: Find and simplify the function values. f(x, y, z)=√x+y+z

A:

Q: Select all of the following tables which represent y as a function of x and are one-to-one. x| 4 8…

A: From the definition of a function, There must not exist such x in its domain such that there is more…

Q: breakeven

A: A point (x,f(x)) is said to be break-even point if revenue is equals to cost.

Q: Consider the functions: f(x) = x², g(x) = x – 1, h(x) = VT, k(x) : and %3D %3D m(x) = x + 1. Write…

A: Solution

Q: Determine the range of f, if f: D → R, where f(x) = x². I. D = (-2,2) II. D = [-7,2] III. D = (-4,2]…

A: I. D = (-2,2) Here the variable x lies between -2 and 2, that is,…

Q: Determine whether the following relations R from A to B is a function or not. If the relation is not…

A:

Q: Determine whether the statement " If f is a function, then f(ax, ay) = a2f(x, y)" ,is true or false.…

A: If f is a function, then f(ax, ay) = a2f(x, y).

Q: Let C be the contour (blue) given in the figure below and let f(z) be any function with If (z)| <…

A:

Q: Let f, g and h be functions defined by f(x)=3x+1; g(x)=- Vx+2 and h(x)=x² –1, find the following: 6.…

A:

Q: The one-to-one functions g and h are defined as follows. g-{(-7, -6), (-5, 0), (0, 1), (4, 6)} h (x)…

A: It is given that one to one functions g and g are defined as follows: g=-7,-6,-5,0,0,1,4,6hx=3x-13…

Q: Given the function h, find functions f and g such that h(x) = (go f)(x). h(x) = (3 + 5æ)³ a. f(x) =…

A:

Q: Refer to the functions f and g and evaluate the functions at x= -4 f={(6,8), (4,5), (-4,-4), (0,0),…

A:

Q: Evaluate the function at the specified points in the figure below

A: g(x,y)=yx2+y2 , (1,3) , (3,-2)

Q: If f(x) = z + 5 and g(z) = z - 5, (a) f(9(x)) (b) 9(f(x)) (c) Thus g(z) is called an function of…

A: Given f(x)=x+5 and g(x)=x-5. a. f(g(x)) As g(x)=x-5 we will substitute the value in place of g(x)…

Q: Determine whether the following

A:

Q: Make a table of values for f(x) = x² - 6 showing function values for x = 4, 6, 8,.. f(x) 4 8 10 12…

A:

Q: Make a table of values for f(x) = x2 - 7 showing function values for x = 4, 6, 8,... f(x) 4 8 10 12…

A: Solution: The objective is make the table of values

Q: The figure defines a function f from A={r, s, t, u} into B={a, b, c, d} in the obvious way. Which of…

A:

Q: Let f(x,y) = 2* + 6xy, find f(0, – 3), f(– 3,2), and f(3,2).

A:

Q: Let f : R → R be a function with the following property: f(x + y) = f(x) + f(y) for all x, Y E R.

A:

Q: Select all of the following tables which represent y as a function of x and are one-to-one. 15 7 1 2…

A:

Q: For the function y = f(x) given graphically below, find all x numbers such that f(x) = 2 Ox = -3, 3…

A:

Q: Determine the domain and range of the function f: {r,s,t,u} ➔ {A,B,C,D,E} defined by f(r) = A, f(s)…

A: Domain of a function is the set of possible values of independent variable. The domain of given…

Q: Determine whether ? is a function from Z to R if a. ?(?) = ±? b. ?(?) = √?^2  +  ? c. ?(?) =1/(?2−4)

A: Solution:-

Q: Let A = {1,2,3} and B = {x,y}. %3D %3D (a) How many functions are there from A to B? (b) How many…

A: Given that                 A=1, 2, 3   and B=x, y We have to find in how many functions are there…

Q: Select all of the following tables which represent y as a function of a and are one-to-one. 1 9. 9.…

A:

Q: f(x, y) = In(4 – x² – y²) + cin IC ö7atll

A: A function has its domain where it is defined.

Q: Determine whether the statement is true or false " If y is a function of t and x is a function of t,…

A: Given:If y is a function of tx is a function of tthen y is a function of x

Q: Let the function f(z) have the property that f'(z) = z+5 If g(z) = f(z') find g'(z). %3D g'(z) =O

A: We have to find g'(x) .

Q: Given the table below, determine whether y is a function of x and if the function is one-to-one. 9.…

A:

Q: Determine the domain of the function f(,y) = /1- a. O {a, y € IR | a? +y? < 1} O {a,y €R | a? +y? <…

A: Given:         fx,y =1-x2-y2        1-x2-y2≥0        1≥x2+y2        12≥x2+y2

Q: Plot the following points for the parent function f(x) = Vx . %3D Plot points for the following…

A:

Q: Assuming f and g are differentiable functions, determine (fg)'(4) if f(4)=3, f'(4)=2, g(4)=-6, and…

A:

Q: If f(x) = z+6 and g(z) z- 6, (a) f(9(x)) = (b) g(f(x)) (c) Thus g(z) is called an function of f(z)

A: f(x)=x+6 g(x)=x-6

Q: Which of the following sets does notdescribe a function? A. {(x.y) |xy– y = x² } B. {(x. Y) |2y° - x…

A: For simplicity, we will plot the relation to identifying whether they are function or not. For (A),…

Differential Equations

Have you ever observed the movement of the satellites and rockets or how the planets go around the sun in their orbits? How will you determine their motion? Definitely they follow some scientific laws and these kinds of problems are framed as differential equations.