Given f(x)=3x-5and g(x) = x' +3x. Perform the requested operation and give the result in simplified form. Give the domain in interval notation. a. (f – g)(x) and its domain b. (x)and its domain С. c. (fog)(x)and its domain

Q: ) Find a function ƒ such that f'(x)= x³ +3 and such that the line y+5x O is tangent to the graph of…

A: Given, f'(x) = x3+3  and the line  y +5x =0 is tangent to the graph of f   Let's assume the function…

Q: Find the slope of the secant line between x=2 and x=5 on the graph of the function f(x)=−2x2+2x+3.

A: We have to find  the slope of the secant line between x=2 and x=5 on the graph of the function…

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A:

Q: For what value(s) of k will the function g(x) = x? - kx + 9 have only one zero?

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A: Obtain the inverse of the given function as follows:

Q: Find f'(x). f(x) = 2x° - 6 ex f'(x) = (Type an exact answer in terms of e.)

A: We have to find

Q: of Find - for the following function. and 5xy f(x.y) = e In (3y)

A: Given: Now,        ∂ ∂ xe5xyln3yTreat y as a constant=ln3y∂ ∂ xe5xy=e5xy∂ ∂ x5xy=ln3ye5xy· 5y

Q: For function i, i(x+4)=3x+1. Find i(-1)

A: Given function is

Q: - 3x + 1, x S 4 Find the value k , if the function ƒ (x) = is continuous at x = 4. -kx + 1, x > 4

A: We will find the value of k as following.

Q: For what value of the constant c is the function f continuous on (-o, o)? { Cx2 2x if x < 5 - x3…

A: Observe that, f (x) has discontinuity at x = 5.If it is continuous at x = 5, then continuous on…

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A: Given : f(x)= 3x4 +4x3-36x2+6343

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A:

Q: # Find a and b so that the function e-ax, x ≤ 0 f(x) = {₁² + 5x + b,x>0 is differentiable…

A: To find out the sum a+b.

Q: Use a formula to express y as a function of t if y = 6x + 4x and x = t- 1.

A:

Q: Find the local and absolute extremum for the functions over their domain: 1. f(x) = x2 – 6x + 8

A: Given

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A: Logarithmic Question

Q: find and sketch the domain for each function ƒ(x, y) = 1/{ln (4 - x2 - y2)}

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Q: Find the Zero and its oodex for the function flz)=1- Ti+Z+

A:

Q: For this function Y=x^3 + 15x^2 -225x prove that we have a point of inflection at x=-5

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Q: function f(x)=2x^3-5x^2+3x+2, find the equation of the tangent line at x=1.

A:

Q: The slope of the line tangent to the graph of f(x) = 19 – 4x² at the point x = -9 18 8 O 152 72 144

A: Given that: f(x)=19-4x2

Q: 2 For what values of x does the graph of f(x) = 2x° + 3x – 180x – 1 have a horizontal tangent line?

A: First we find the derivative of f(x), the slope of f(x) for horizontal tangent is 0 and the…

Q: For the f(x) = 1/1-X^2 and g(x)= x^2/1-X^2 A) shows that these functions have the derivative B) what…

A: We need to find relation between f and g.

Q: find all possible functions with the givenderivative. y' = 2x - 1

A: Given y'=2x-1 that is  dydx=2x-1 Integrating with respect to x, ⇒y=x2-x+C Where C is the constant of…

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A: h(x)=ln x2

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A: we have to find the domain of the given function. f(x)=ln(4-x)

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A: Find all the intervals for where the function is increasing and decreasing

Q: Find the domain of the function: f(x) = ln(3 - x)

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Q: Find the values of a and b so that f will be differentiable at x = 3.

A:

Q: 1 Find the distance between the two values of x at which the function is discontinuous. x²-3x + 2

A: The function given is ,f(x) = 1x2-3x+2f(x) is discontinous when,x2-3x+2 = 0Using quadratic formula,x…

Q: Next, differentiate the given function y = X 8x + 37 and write as a single fraction completely…

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Q: Find the value for k so that the function will be continuous at x = 2. 4x + 16 if x 2

A: The function fx is continuous at x=a, if limx→a-fx=limx→a+fx It is given that fx=4x+16if…

Q: In certain conditions, the atmospheric pressure (p) in the height (h) is given by p=29e-0.000034h.…

A: It is given that the atmospheric pressure in the height is given by the function…

Q: The function f(x)=(1/(x+1))+4 is decreasing on what interval(s)?

A: Consider the function  fx=1x+1+4

Q: The slope of the line tangent to the graph of f(x) = 18 – 5x² at the point x = -8 O 20 O 10 O 160 O…

A:

Q: find all possible functions with the givenderivative. y' = -1/x2

A: Given: y'=1x2

Q: Find the slope of the secant line between x=3 and x=5 on the graph of the function f(x)=−2x^2+2x+5.

A:

Q: find all possible functions with the givenderivative. y' = 4x - 1/√x

A: Giveny'=4x-1x  To Find: All possible function with the above derivative

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A: solve the equation for value of x.

Q: Find k so that the function f(x) = x² + kx will be tangent to the line y = 2x-9

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A:

Q: Find all the values of x where the graph of f(x) = 2x³-36x2 + 192x 9 has a horizontal tangent line.…

A: topic - derivative of a function and point of horizontal tangent line

Q: For the function f(z) = ¹, the point z 1-e Z = 0 is

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Q: x², -2sx<1 (x+1, 1sx<2 For the piecewise-defined function f(x) = }

A: fx=x2,-2≤x&lt;1x+1,1≤x&lt;2

Q: 3. Given the function g(x) = x - 2x2 + x, find the interval(s) when g is concave up and decreasing…

A: We have given a function g(x).  We have to find the interval where g is concave up and decreasing at…

Q: ind the equation of the osculating circle at x=2 for y= 1/4x^2-x. Draw the circle

A: