Find two functions f and g such that (f ∘ g)(x) = h(x)

Q: True or false: The graph of the reciprocal function f(x) =1/x has a break and is composed of two…

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Q: 11) Sketch the graph of the piecewise function below. |x + 8| + 3 f(x) = -(x-1)² -3 -5sx< 3 2/3x + 2…

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Q: 8. Determine algebraically if the function is even, odd or neither. y = -2' - |-2°|

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

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Q: 3 Show that the function f(x) = - 2x + 5x has no relative extreme points. Relative extreme points…

A: Consider the function fx=13x3−2x2+5x Differentiate fx=13x3−2x2+5x with respect to x…

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

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Q: 1. Let f(x) = -(x - 3)2 + 1. Find the vertex. Give the range of the function.

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Q: Sketch an odd function with a positive leading coefficient having all of the following features:…

A: We have to draw graph of given odd function.

Q: Find a formula for f-(x) and (f-1)'(æ) if ƒ(x) = -V5 – x f-' (x) = (5-1)'(x) =

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Q: 3 Determine the intervals for which the function f(x) = x° + 18x +2, is decreasing.

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Q: sketch the approximate shapes of the graph of the two functions on the same axes without using a…

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Q: 7) Sketch a graph for f(x) 3 + 2-x

A: To plot the given function:

Q: 3-64 -If f(x)=04 is the function continuous at x=4 x-4

A: If a function f(x) is given and we have to check continuity at x=a then we have to find LHL, RHL and…

Q: 2, if x 0 Evaluate the piecewise function at the indicated values from the domain: f(x) = at x=-8…

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Q: Suppose f(x) is a twice-differentiable function which is positive and decreasing for all real…

A: Consider the given conditions for f(x) and assume the graph for function f(x) for the given…

Q: 1. Find x- and y- intercepts of the graph of f, if it has any.

A: Note: As you have posted the multiple numbers of questions, so we are going to solve the 1st…

Q: sketch the approximate shapes of the graph of the two functions on the same axes without using a…

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Q: The graph of f(x) = is (increasing/decreasing) over its domain. 3 ()

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Q: 1. Use the limit definition of the derivative to find g'(x) if g(x) = 2x² – 6x + 13.

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Q: For what value of the constant c is the function ƒ continuous on (-∞, ∞)? cx² + 2x if x 2.

A: We know :- Limit definition at x=a  ⇒limx→a-f(x) =limx→a+f(x)  if function continous at x=a then…

Q: 7. If, for all real numbers x, f'(x) 0, which of the following curves could be a part of the graph…

A: For all real numbers xf'(x)&lt;0 ⇒f(x) is decreasing for all real numbers.f"(x)&gt;0 ⇒f(x) is…

Q: 5. Consider the following piecewise function. x-4, if x>2 f (x) = {- 1, if x = 2 x² - 4, if x<2 a)…

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Q: 66. What will be the function g(x) resulting from normalizing the function f(x) = x³ − x4 defined in…

A: To find : function gx resulting from normalizing the function fx=x3-x4 defined in the domain 0, 34

Q: (1+ 3x X 1

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Q: Determine the points of inflection on the graph of f(x)= 1 x²+3 -1 and 2 -1 and 1 2 and -2 None of…

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Q: 17. Find the end behavior for f(x) = -3x - 2x -7 A. x- +o, f(x) +0 x -o, /(x) - - B. x-+o, /(x) -00…

A: “Since you have asked multiple question, we will solve the first question for you. If you want any…

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

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Q: 35. Estimate any extrema of the function given by g(x) = x3 – x3.

A: The extrema of a function are the maximum and minimum values of the function. To find the critical…

Q: sketch the approximate shapes of the graph of the two functions on the same axes without using a…

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Q: Suppose that f(x) is a differentiable function such that f(3)= 8 and f'(3)=-2. If g(x)=xf(x), then…

A: Product Rule of differentiation : d(u.v)dx = u.dvdx + dudx.v

Q: 2. Use the graphs of y=f(x) and y= g(x) to sketch the graph of y=h(x). Hint: Estimate the function…

A: answer is in next step.

Q: 1. Let f(r) = 1– x². (a) Sketch a quick graph of f for -2 <r < 2.

A: The given function is The graph of the function is inverted parabola with vertex going in upward…

Q: 7. Give an example of two functions h(x) and g(x), such that (h o g) (x) does not exist.

A: we need to find two functions h(x) and g(x), such that (hog)(x) does not exist. Let us take two…

Q: (4) Sketch the graph of a function f(x) satisfying (a) f(x) 2 and for x 0 for x between -1 and 2,…

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Q: 5 Find the domain, asymptotes, x and y-intercepts of the followingrational function:f(x) = x+1/x

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Q: 16. Sketch the graph of f(x)=(4-x)(x+1)(x+3)*. Be sure to label all x- and y-intercepts.

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Q: 0. if a 2

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Q: 13. Use the idea of transfr-mation to sketch the function y = -2f(x+2) + 3 if the graph of y = f(x)…

A: Given: The graph of y=f(x) is

Q: 70 The function f(x) = has a removable discontinuity at a = 0. To remove the 10+22 +2z…

A: -&gt;Given functionf(x)=7010+x2+x3-6xx3+2xNow we want to define f(x) at x = 0 in such a way that the…

Q: function

A: We are given a function : f(x)=x2-2x+2x-3 We have to determine the domain of given function where…

Q: 3. Give an example of a function with discontinuities at x =1 and x = 5.

A: To Find : A function that has discontinuities at x=1 and x=5.

Q: 5) The graph of the function f(x) = 4-x has an inflection point at

A: Given: fx=x4-x We know that for any function, inflection point are points where second derivative of…

Q: The graph of the second derivative, f"(x), is given. > 10 6 -1 -2 -4 -6 -8 -101 Determine the…

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Q: . Find the length of the graph of the function f (x) =x* + x2 -<x < 3. on the ir

A: The length of the graph of y=f(x) from x=a to x=b is given by:∫ab1+f'(x)2dx f'(x):…

Q: If the graph of a function f(x) is decreasing over the interval (a, b) then which of the following…

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Q: The graph of f(x) = x² is transformed to create the graph of h(x) = 2f(x). Which graph best…

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Q: 7- -6 -5 -2 4 -5 -6 -7

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Q: Use the graph of the function f to decide whether the value of the given quantity exists. 3 -4 -2…

A: According to company policy we are allowed to provide solution for only first 3 sub parts. If you…

Q: 5. Find the value of k that makes the following function continuous. f(x) : ={2x - 1,if x2-1

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Limits

When it comes to calculus, limits are considered to be a very important topic of discussion. The main importance of limit lies in expressing the value of a function as it gets closer to a certain value. Also, limits can help you to understand other topics, such as continuity and differentiability better. In a broader sense, every calculus notion is a limit. Other branches of calculus have also been derived from limits.