2. The function f and g are given by f(x) = In x and g(x) = e* +2 a) State the domain and range of f and g. b) Sketch the graph of f and g. Label the x -intercepts and y -intercepts. c) Find fg(x) and gf (x).

Q: Ax, y) = In(x +y)

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A: Given   y = sin (x3) ....(1)   , (1, 2)

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Q: IS The function f(x)=\x3 Find The value of K, to continue The Function Con tinuous in intervaln X-2…

A: Answer

Q: Prove, without graphing, that the graph of the function has at least two x-intercepts in the…

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Q: For Exercises 43 and 44, sketch the graphs of f and ƒ ° f. 2, -4 < x < -1 -1 <x < 1 1 <x< 2 43. f(x)…

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Q: Use the vertical line test to identify graphs in which y is a function of x.

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A: The given function is: g(x)=3x+4

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Q: 1. What does it mean to say that the equation +y 6ry defines y as an implicit function of r? %3|

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Q: 2. Given that f(x) = Vx+1 and g(x) =x² -9, find |(x) and give its domain in interval notation.

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Q: The graph of g consists of two straight lines and a semicircle. Use it to evaluate each integral. y…

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Q: The slope of the line tangent to the graph of f(x) = 15 – 3a2 at the point z = -8 %3D 48 96 O 12 O…

A: Solution is given below : Answer: 48

Q: 14. Use the curve sketching procedure to analyze the function. a. y-x'+x²-20x а. 1+x? b. y=- 1-x?

A:

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A: The graph passes through (1,1). So at x=1, f(x)=1

Q: lim 3i 4 +

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Q: Please

A: For concave downward, f''(x) &lt; 0 f(x) = (1-1/x)2 = 1 - 2/x + 1/x2 f'(x) =2/x2 - 2/x3 f''(x) =…

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A: The given function is gx=32-x  exist in the interval (-∞,32] and does not exist in any other…

Q: 5. If f(x) = ax* + bx' +cx² + dx +e, determine a, b, c, d and e so that the graph of f will have a…

A: 5) Given:   f(x)=ax4+bx3+cx2+dx+e As f(x) passes through origin (0,0) then substituting (0,0) in…

Q: 4. Consider the functions g(x) = and . Determine (12)- (}),

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Q: The function g(x) is obtained by shifting the graph of y=x2. (a) If g(3)=36, give a possible formula…

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Q: 1. Can Rolle's Theorem be applied to y = (x – 2)5 on the interval [0, 4]? Justify.

A: we will see how to proceed

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Q: Consider the relation x2z2 = arctan (xyz) + 4, which defines z as an implicit function of x and y,…

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Q: 1. Can Rolle's Theorem be applied to y = (x – 2)3 on the interval [0, 4]? Justify.

A: Check differentiability at x=2

Q: Sketch the graphs of the function f(x) = cos x. y y 2 2 f X 3X -27 2 -2- -2- y y 2- f X -27 - 2 2 -1…

A: We know, cosx = 0, if x =(2n+1)π2; n∈ℤcosx = (-1)n, if x =nπ;  n∈ℤ

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A: we have been given the coordinates (-4,0), (-2,-2), (0,0), (2,2), (4,0) for the graph y=f(x) first…

Q: 46. Let f(x) = x³ - 4x² . Find the points on the graph of f where the tangent %3D line is…

A: 46. The given function is fx=x3-4x2. Differentiate fx with respect to x. f'x=ddxx3-4x2=3x2-8x Now,…

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Q: The graph of g consists of two straight lines and a semicircle. Use it to evaluate each integral. y…

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Q: Find the constant a such that the function is continuous on the entire real line. (9x², Flx) = {9x?,…

A: Given function is : fx=9x2    ,      x≥1ax-6   ,    x&lt;1 Here given that function is continuous…

Q: The graph of g consists of two straight lines and a semicircle. Use it to evaluate each integral. y…

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Q: Let P=(x,y) be a point on the graph of y=square root of x a) Express the distanced d from P to the…

A: Please refer to the image below.

Q: What is the largest interval in the function f(x) = x² - 2x + 1? A. (-∞, 1) B. (-∞, 0) C. (1, ∞)…

A: Function -  parabolic function    Option A is the correct option.

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Q: 2. Sketch the graph of the function (b) ƒ(x, y) = Vx² + y? – 1 -

A: our objective is to draw the graph.

Q: The graph of a function y = f(x) in the xy-plane is the set of all points _______ that satisfy the…

A: Given: The graph of a function y = f(x) in the xy-plane is the set of all points _______ that…

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A: Line integral is integral of some function along a curve or path. Any field for which the line…

Q: (b) Use the result of part (a) to find the direction in which the function f(x, y) = x³y - x²y4…

A: Given:

Q: Use the graph of f(x) = ex to obtain the graph of g(x) = eX. %3D %D

A: