Functions Questions and Answers

The second order ordinary differential equation d²y/dt² + 3dy/dt + 4Y=sin(t) is defined over the domain 0 ≤ ≤ 6, and is to be solved numerically subject to the initial conditions (0) = 0, dy(0)/dt = 4, where X is the exact solution. (1) Reduce the above second order ordinary differential equation to a system of first order ordinary differential equations.

Determine the domain D and range R of the following relation from its graph, and tell whether the relation is a function. The domain is The range is

Consider the curve (in the plane) formed by: the line segment from (2, 0) to (5,0), the part of the circle of radius 5 (about the origin) from (5,0) to (0, 5), the line segment from (0, 5) to (0,4), and the part of the parabola y = 4x² from (0, 4) to (2,0). Orient this curve so that the direction of travel on the first line segment is from (2,0) to (5,0). Let f(x, y) = In √x² + y². Calculate the flux of Vf across this curve (with the given orientation).

Find the product. Leave the result in trigonometric form. (Let 0 ≤ θ < 360°.) [9/7(cos(135°) + i sin(135°))][1/7(cos(60°) + i sin(60°))]

The only New Zealander to appear on the country's banknotes while still alive were famed mountaineer Sir Edmund Hillary, were was being had been

Wrote her essay by hand instead of on the computer, Ingrid was able to concentrate without the distraction of constant Internet access. Wrote Write Written Writing

Uma. __ originally from India, wore a sari to the party. is who is she she is

What are the domain and range of this linear function? f(x)=-3x+2 Domain: x ≥0 Range: -∞<y<∞ Domain: x≥0; Range: y≥2 Domain: 0<x<∞ Range: -∞<y<∞ Domain:-∞<x<∞0; Range: V=2

For f(x) = x/x+1 and g(x)= 4/x, find a. (fog)(x) b. the domain of fog a. (fog)(x) = Simplify your answer.) What is the domain of f o g? A. (-∞, -4)U(-4,0)U(0,∞) B. (-∞,0)U(0,4)U(4,∞) C. (-∞, -1)U(-1,0)U(0,∞) D. (-∞,∞)

Given the functions f(x) = 1/x^2+3x with the domain {x|x ≠-3 and x ≠ 0} and g(x) =1/√x with the domain {x|x >0}, what is the domain of (gof)(x)? a) {x|x > 0, x = R} b) {x|x ≠0, x = R} c) {xx<-3 or 0 < x, x = R} d) {x|x > 3, x = R}

The diagram of a rectangular prism with a square base is given below. Assume that the surface area of the prism is fixed at 96 m². Find the width and height of the prism that will maximize its volume. The surface area of the prism = 2(width)2 + 4 width . height.

Let f(x)= 10x + 6. Find f(1/2)

For f(x)=√x and g(x) = 4x+1, find the following composite functions and state the domain of each. (a) fog (b) gof (c) fof (d) gog (a) (fog)(x) = (Simplify your answer.) Select the correct choice below and fill in any answer boxes within your choice. A. The domain of fog is {x}. (Type an inequality. Simplify your answer. Use integers or fractions for any numbers in the expression.) B. The domain of fog is all real numbers. (b) (gof)(x) = (Simplify your answer.) Select the correct choice below and fill in any answer boxes within your choice. ... A. The domain of g of is {x}. (Type an inequality. Simplify your answer. Use integers or fractions for any numbers in the expression.) B. The domain of g of is all real numbers. (c) (f of)(x) = (Simplify your answer.) Select the correct choice below and fill in any answer boxes within your choice.

Solve the following system of equations. 4a - 40b = - 18 8a + 36c = 20 80b + 24c = 54 Select the correct choice below and, if necessary, fill in the answer box to complete your choice. (A) The solution is ______ (B) There are infinitely many solutions. (C) There is no solution.

The function f(x) =∛x⁵-7 is one-to-one. (a) Find the inverse of f and check the answer. (b) Find the domain and the range of f and f^-1

Given the polynomial function f(x)=(x-1)²(x+2), find: a). End behavior. x →∞, f(x) →__________ x →-∞, f(x)→__________ b). Zeros.__________ c). Degree and maximum number of turning points. Degree:___________ Max # Turning Points:__________ d). Local Extrema. Local Max(s):________ Local Min(s):_________ e). Graph the function.

The function f(x) = 9x is one-to-one. (a) Find the inverse of f and check the answer. (b) Find the domain and the range of f and f^(-1). (c) Graph f, f^(-1), and y=x on the same coordinate axes. (a) f¯¹(x) =_________ (Simplify your answer. Use integers or fractions for any numbers in the expression.) (b) Find the domain of f. Select the correct choice below and, if necessary, fill in the answer box to complete your choice. A. The domain is {x|x≥_______}. B. The domain is {x|x≠_______ }. C. The domain is {x|x≤________ }. D. The domain is the set of all real numbers.

What is the domain of f(x) =x-5/x² + 6x-16? Select the correct choice below and, if necessary, fill in the answer box(es) to complete your choice. (A). The domain is {x|x≥____≤x≠______} (B). The domain is {x|x≠___}. (C). The domain is {x|x≤______ ,x≠_____ .}. (D). The domain is {x _____} (E). The domain is the set of all real numbers.

Consider the functions f(x) = 2x − 8 and g(x) =x/2 +4. (a) Find f(g(x)). (b) Find g(f(x)). (c) Determine whether the functions f and g are inverses of each other. (a) What is f(g(x))? f(g(x)) = __________

For f(x) =x-4/x+7 and g(x)=x+5/x-8 find the following composite functions and state the domain of each. a). fog b(. g of c). fof d). gog

Given f(x) = 9/x+7 and g(x)= ∛x find the following expressions. (a) (fog)(4) (b) (gof)(2) (c) (fof)(1) (d) (gog)(0)

The function f(x) =(x²-9)/3x², x>0, is one-to-one. (a) Find its inverse and check your answer. (b) Find the domain and the range of f and f^(-1). (a) f^(-1)(x) =____________ (Simplify your answer.)

Graph the rational function as a translation of f(x)=1/x. Identify the vertical and horizontal asymptotes and state the domain and range f(x)=4/(x-4) Find the vertical asymptote(s). Select the correct choice below and, if necessary, fill in the answer box to complete your choice. a) x=_______ (Type an integer or a simplified fraction. Use a comma to separate answers as needed.) b). There is no vertical asymptote Find the horizontal asymptote(s). Select the correct choice below and, if necessary, fill in the answer box to complete your choice. a) y=______ (Type an integer or a simplified fraction. Use a comma to separate answers as needed.). b). There is no horizontal asymptote The domain of f(x) is ________ (Type your answer in interval notation.) The range of f(x) is _____ (Type your answer in interval notation)

Given the functions ƒ(x)=(x−2)² and g(x)=√x+2, show that ƒ and g are inverses of each other by showing that f(g(x))=x and g(f(x))=x.

Differentiate the following function and factor fully. f(x) = (x + 4)³(x - 3)⁶ a) 3(x+5)(x+4)²(x-3)⁵ b) 3(3x+5)(x+4)²(x-3)⁵ c) (9x+15)(x+4)(x-3) d) 6(x+5)(x+4)³(x-3)⁴

The line has an equation of y=2x intersects the curvey² = 8x, Determine the centroid of the area from the y-axis. A. 7/9 B. 1/3 C. 2/7 D. 4/5

Determine whether the equation could represent exponential growth or decay. y=e^x growth decay neither

State the poles of the rational function below 4s +9/2s - 18

Let x = ln(1+t), y = tan-¹t be the parametric representation of a plane curve. 1. What are the possible values of x and y 2. Find a Cartesian representation of the curve

Read the statement or passage and then choose the best answer to the question. Answer the question on the basis of what is stated or implied in the statement or passage. Passage Mammoth Cave in Kentucky is the world's most extensive cave system. It was first advertised in 1816. making it the second oldest tourist attraction in the United States. Stephen Bishop, an African American slave and a tour guide, was one of the first people to make extensive maps of the cave, and he named many of the cave's features, such as The River Styx and The Giant Dome Question The author's main purpose is to provide the biography of a famous person practical information for travelers historical facts about a place technical details regarding cave exploration

The scientists who discovered the skeleton of "Ardi"-short for Ardipithecus ramidus-think she may represent a breakthrough in the study of human origins. The fossils show that Ardi walked upright, and that her teeth resemble modern human teeth more closely than they do those of a chimpanzee. Curiously, though, her feet were capable of grasping, something chimps need in order to climb in trees. "This is huge," says Carol Ward of the University of Missouri. "This is the biggest discovery since the 'Lucy' skeleton of the 1970s." Question The passage implies that, in addition to being able to walk upright like a human, "Ardi" could climb like a chimpanzee eat like a chimpanzee run like a chimpanzee communicate like a chimpanzee

Find the equation of the line using the point-slope formula. Write the final equation using the slope-intercept form. perpendicular to 5y = x - 4 and passes through the point (-2, 1)

In an automated production process a hydraulic ram moves a 180 kg crate with a force, F = 700 - 150s Newtons, where s = distance in meters. Determine the speed of the crate in meters per second after it has moved a distance of 2 m. In the addition, the coefficient of kinetic friction between the crate and the surface is 0.26 and the crate's initial condition is s = 0, v = 0.

The table below shows some input-output pairs for an exponential function g. X 1 2 3 4 5 g(x) 244.8 416.16 707.472 2044.59408 i. Determine the 1-unit growth factor for g. ii. Determine the 1-unit percent change for g. iii. Determine the initial value for g (the output value when the input is 0.) g(0)= iv. Write a function formula for g. g(x)=

An exponential function f(z) = a - b passes through the points (0,9) and (2, 144). What are the values of a and b? a= __and b=__

Given that f(x)=x²- 9 and g(x) = 8x + 1, find (fg)(-1/8) if it exists. Select the correct choice below and, if necessary, fill in the answer box to complete your choice. A. (fg)(-1/8)= (Simplify your answer.) B. The value for (fg) (-1/8) does not exist.

Given the function f(x)= 7x+1 , x < 0 7x+ 2 ,x ≥ 0 Calculate the following values: ƒ( − 1) = f(0) = f(2)=

Let f(x,y)=x² - 4xy-y². Compute f(3,0) and f(3,-7). f(3,0)= (Simplify your answer.) f(3,-7)= (Simplify your answer.)

Graph the following function. y = sin (x +π/2)

If the tangent and binormal at a point of the curve make angles θ and φ respectively with a fixed direction, prove that sin θ dθ/ sinφ dφ=-k/t

Name the corresponding sides and the corresponding angies of the following pair of similar triangles.

Write a rational function that goes through the dashes on the graph. When you finish, press 'Graph and submit response. Graph and submit response

- matrix A. Determine if A is diagonal, symmetric, skew-symmetric, or none of these. Let A be a 3 x 3 matrix such that the ij-entry aij of A is given by aiji.j. Write the $803 voM 73:200

Evaluate f(-3) in the piecewise function below. x - 2 for x≤-3 f(x)= 8 for-3<x≤5 -x+10 for x>6 a)-3 b)-2 c) -5 d) 8

If the length of a rectangle is increased by 6 inches, the area becomes 135 square inches. Determine the original length of the rectangle.

Which function has an period four times the length of f(x) = -4(cos8x) + 2? a. f(x) = -4(cos32x) + 5? b. f(x) = -16(cos1/2x) + 2? c. f(x) = -4(cos8x) + 8? d. f(x) = -3(cos2x) + 2?

Find the equation of the tangent to the function f:R → R where f(x) = x^2 + 5x on the point (-1,-4).

A circle passes trough A(7,8), B(3,10) and C(0,9). (Hint: include a diagram) a) Determine the center of the Circle b) Write the equation of the circle

Find the equation in standard form of the ellipse, given the information provided. Center (-4, 2), vertices (-10, 2) and (2, 2), foci at (-7, 2) and (-1,2)

A person invested $4,300 in an account growing at a rate allowing the money to double every 12 years. Write a function showing the amount of money in the account after t years, where the annual growth rate can be found from a constant in the function. Round all coefficients in the function to four decimal places. Also, determine the percentage of growth per year, to the nearest hundredth of a percent. Function: f(t) =________ _______ _________ % increase per year