Let f (x) = x2 − 2x. Determine a domain on which f −1 exists, and find a formula for f −1 for this domain of f .

Q: Show that f (x) = (x2 + 1) −1 is one-to-one on (−∞, 0], and find a formula for f −1 for this domain…

A: The given function is fx=x2+1-1. This implies that, fb=fab2+1-1=a2+1-1b2+1=a2+1b2=a2b=a     on -∞, 0…

Q: Consider the function f(x)=xe−9x,0≤x≤2. On this interval, ff has a minimum value equal to: which is…

A: Given fx=xe-9x 0≤x≤2

Q: Find the domain of f(x) = 1/x and discuss the behavior of f near any excluded x-values.

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Q: I'm stuck on this question and I don't know how I should be approaching this. What should I do?

A: The given function is

Q: For any function f(x), if g(x) =f(x2) then  is g(x)  always increasing?

A:

Q: Let f(x)=ln(2−x2). Find all values of c in the open interval (−1,1) such that f′(c)=0.

A: Here given function Since the is differentiable in the interval (-1, 1) then it is also continuous…

Q: Determine the domain of the function and prove that it is continuous on its domain using Theorems…

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Q: I'm stuck on this question and I don't know how I should be approaching this. What should I do?

A: Given: Since every differentiable function must be continuous.

Q: f(x) = 4x^3 − 3x^2 − 18x + 5. (e) Find the inflection points of the graph of f, if any.

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Q: Determine the domain of the function and prove that it is continuous on its domain using Theorems…

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Q: 8. Find all the points in the interval [1,5] for f(x) = -x² + 6x – 6 such that the function verifies…

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Q: Let f(x)=x2+2x. Find all values of c in the interval [−2,0] such that f′(c)=0.

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Q: Let h(x)=f(x)g(x) where f(x)=−4x^2−5x+1, g(1)=−5, and g′(1)=−4 what is h′(1)?

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Q: The function h(x)= 1 over x-8, can be expressed in the form f(g(x)), where g(x)= (x-8) , and f(x))…

A: use composition of function to find the function f(x).

Q: Let f and g be the functions defined by f : R → R+ ∪ {0} with f (x) = x2 and g : R+ ∪ {0} → R with…

A: (fog)(x) is the value of the function f(x) at g(x) (fog)(x)= f(g(x))

Q: Find a formula for f®(x) if f(x) =In(x – 1).

A: Given that,

Q: (a) Let f(x) = x³ +x² + kx, k a constant. For what val- ues of k is f one-to-one? (b) Let g(x) = x³…

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Q: 2.) For the functions f (x) = 3x + 5 and g(x) = 2x – 8 find (E) (x) and give its domain in interval…

A: Consider the functions  f(x)=3x+5g(x)=2x−8

Q: For any function f(r), if g(x) = f(x²) then g(z) is always increasing.

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Q: Let f(x) =xe^x^2. Find f'(x).      (xe to the power of x, which itself is to the power of 2.)

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Q: 2 For the function f(x) = -x', find f'"(x), f'"(0), f'"(1), and f"(- 1).

A: To find the double derivative for the given function.

Q: Find the value of k so that the function 5x+3 if x<3 f(x) =. kx2 if x 23 is continuous everywhere?

A:

Q: Find the values of k that make the function continuous. k2 – 22x, x > 11 - f (æ) = kæ, x < 11

A: to find the values of k the function is to be continuous for x=11 value of k is 22 or -11.

Q: Over the interval (0,2), the function f(x) = (-x²) e*

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Q: find the largest domain for f(x) = (x-3)2   with an upper x bound of 8 such that the function f is…

A: fx=x-32 Differentiating with respect to x, we get f'x=2x-3 Now function is non decreasing in the…

Q: Let f (x) = 2x3 – 0.0064x? – 1.5x + la (a) Indicate that f(x) = 0 has a root in the interval [-3, 0]…

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Q: , for x 1 Let f(x) be a function de fined by f(x)3= Discuss the contuniuty of f andf".

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Q: Let f (x) = x2 − 2x. Determine a domain on which f−1 exists, and find a formula for f−1 for this…

A: The given function is

Q: Find the function f(x) such that f' (x) = x²e# with f(0) = 0. O (x² - 2x - 2)e* + 2 O (x2 + x + 2)e*…

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Q: Find x for which f(x) is not continuous: 3 x-1 f(x) =-+ x'x2 -1

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Q: Determine whether the function f (x) = {: —х in — 1 <x<0 in 0<x < 1 is even or odd,

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Q: Let F(x) = Vg(x). Find a formula for F'(x) in terms of g(x) and g'(x). Use your formula from (a) and…

A: Fx=gx Differentiating with respect to x, we get F/x=12gx·dgxdx    ∵dxdx=12x=12gx·g/x=g/x2gx

Q: Let h(x) = f(x)g(x). If f (x) = 3x² – x – 4 and g(x) = -x² + 2, what is h' (-1)?

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Q: Show that the function f : R → R given by f(x) = x3 is injective.

A: To show the given function is injective(one-one), first calculate the value of function at two…

Q: 8. For the function f(x)=3x+5-11, find the values of x such that f(x)=0.

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Q: Find the value for k so that the function will be continuous at x = 2. 4x2 – 12x + 8 6 if x 2

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Q: Let h(x)=f(x)g(x). If f(x)=2x2+1,g(1)=0, and g′(1)=−1, what is h′(1)?

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Q: let f be the function given by f(x)=kx/(x^2+1), where k is a constant.  For what values of k, if…

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Q: Let f(x) = Vx - 1 g(x) = v2- x obtaind )(x), and the domain of (x),

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Q: Give an example of a function f : R → R that is continuous at x if x is an irrational number, but it…

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Q: f(x)=- %3D x² +6x+9

A: A function f(x) is said to be continuous at a point 'a' when the function is defined at that point…

Q: Then the value of k for which f(x) is continuous for all real values of r is

A:

Q: Show that a function f(x) = ∑ ∞n=2 (1/x-nπ + 1/nπ) is well defined on [0, π]. That is, prove the…

A: Given function,

Q: Let f(x, y) = -e2"-y + In(3x – y). Find the domain of this function.

A:

Q: Express the function h(x)=1x+8h(x)=1x+8 in the form f∘gf∘g. If g(x)=(x+8)g(x)=(x+8), find the…

A: The given function is h(x) = x + 8.We have to express it as a composition of two functions f(x) and…

Q: The function of f is increasing on I if ______ when x1 < x2.

A: We have to find when function is increasing

Q: Determine what, if any, value to assign to f(a) to make f continuous at x2-5x+6 f(x) = %3D ;a= 3 x-…

A: We have to find the value

Q: Show that f(x)= has a zero over the interval [0,1]. f(x) = x³ x2 – 3x +1 - Your answer

A: Explanation of the answer is as follows

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.