find f-1 (x) and the inverse function of x b) what is the domain of the f(x) in interval notation and what is the domain of the f-1(x) in interval notation? c) what is f (1)? d) what is f-1 (-8)

Q: Find the functions and their domains. (Enter the domains in interval notation.) f(x) = 9x + 8,…

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Q: Sketch the graph of a function f that is defined over all real numbers and that is decreasing on the…

A: Given: f(x) is decreasing on the interval -2,3. f(x) is concave down on the interval -2,2 f(x) is…

Q: Determine the intervals on which the function is increasing and the intervals on which the function…

A: According to question given thatf(x)=1-x2x

Q: Let f be a function that is positive and differentiable on the entire real number line and let g(x)…

A: Given: f(x) >0 , f is differentiable on the entire real line  and g(x) =ln(f(x)) g is increasing.

Q: Domain of f(x) has all reals except? Let f(x)=- x-2 Type just the number. 2

A: Topic:- function  Domain :- The domain of a function f(x) is the set of all values for which the…

Q: The function f(x) = √√x-2 + √√4-x is. increasing on its natural domain O increasing on (2, 3) and…

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Q: What does it mean if a function f is increasing on an interval?

A: Let the given function be y = f(x) And the interval be I.

Q: f(x) = -x/x-1, show that ½[f(x) + f(-x)] = f(x2)

A: The given function is fx=-xx-1.

Q: 44. Find f(x) if f(x) = 1/(2 - x).

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Q: Suppose f is a function with range (-∞, ∞) and g is a function with domain (0, ¤). Is it possible…

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Q: find the interverse of the function on the given domain. (Enter the domain using interval notation.)…

A: For (a),

Q: Find a formula for the inverse function f' and verify that 50 (fof *)(x)=(f*of)(x)=x, if f(x)=; Also…

A: Given that  f(x)=501+1.1-x--- (1) To find f-1(x) Replace f(x) as y in (1) y=501+1.1-x Swapping the…

Q: Use algebraic notation to describe how to transform the blue function into the red function. 6+ 2-…

A: Consider

Q: Use algebraic notation to show how to transform the green function into the purple function. 2 -5 -2…

A: We are given a function in green i.e.…

Q: Consider the function f(x)=4-5x2 on the interval [-1,8]

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Q: Consider the function f (x) = (x+3) for the domain[-3, 0). Find f (x), wheref -1 is the inverse of…

A: Consider the given function. f(x)=(x+3)2 The domain is given as [-3,∞). The objective of the problem…

Q: Find the inverse of the function on the given domain. (Enter the domain using interval notation.)…

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Q: Determine the intervals in which the reciprocal function of the increasing. f(x) = x² +1 0 (-1,00) 0…

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Q: show that f is one-to-one on the given interval and thereforehas an inverse function on that…

A: the given function is  f(x)=(x-4)2,  [4,∞)

Q: Is it possible for a function f to attain only positive values (that is, f(x) > 0 for all x) and…

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Q: I realized that continuity of function is _______________________________________ I can apply what…

A: A function is continuous at a point if the three following conditions are met: 1) f (a) is defined.…

Q: What is meant by Identity function in terms of algebra?

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Q: 9. Algebraically find the domain of the function in interval notation. Show your work. g(x)

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Q: Sketch the midline and the graph of the function f(x) = 2 - 3 sin %3D 8- 7- 5- 4- 3 -5 -4 -3 -2 -1 4…

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Q: tan x – 2 If f(x) sec x f'(x) = f'(4) =

A: f(x) = (tan x - 2)/sec x f(x) = (tan x/sec x) - (2/ sec x)        = (sin x * cos x /cos x) - (2 cos…

Q: f(x) is a function,          when,Domain f(x)=rang f(x) then,function f(x)=?

A: As we know the definition of One - One and onto function :- If Domain f(x)= Rangef(x)  Then f(x) is…

Q: A function fC) is defined as f) = --Sr. What is f(-3)? %3D

A: Explanation of the solution is given below..

Q: A piecewise function f is defind by [1-x, x1.

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Q: tan x – 4 - If f(x) = sec x f' (x) = f'(1) =

A: We will use relationship between different trigonometric function to solve this.

Q: 4 find the domain of the composite function, f(g(x)). 1 Given f(x) and g(x) 4 x – 3 Write your…

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Q: The domain of a one-to-one function g is [ - ∞, 0 ] , and its range is [0, ∞ ]. State the domain and…

A: Graphs of inverse functions have a domain and range just like any other graph of a function. The…

Q: Differentiate the function.   f(x)  = x In x -x

A: Given, fx=x ln x-x

Q: Find the inverse of the function on the given domain. (Enter the domain using interval notation.)…

A: Given,         fx=x+42-8 , [-4,∞)

Q: The intervals of increasing and decreasing for the function f(x) = (x – 4)² + 8 is increasing in [5,…

A: The given function is: f(x)=(x-4)2+8

Q: 19) Find f' if f(x)= sec² x 83√x

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Q: True or False The cube function is odd and is increasing on the interval (-∞,∞)

A: Explanation:' The cube function is f(x)=x3 An odd function is the function that satisfy this…

Q: Prove that (f^-1)^-1= f, where f^-1= inverse notation

A: A function is said to be invertible function when it has an inverse .

Q: Find the inverse of the function on the given domain. (Enter the domain using interval notation.)…

A: f(x)=(x+4)2-8 To find inverse , replace f(x)by y then swap the variables x  and y .  f(x)=(x+4)2-8…

Q: Determine where the function discontinuous. [-(x+2)² +1→x≤-2 f(x)=x+1→-2≤x≤3 [(x-3)² −1→x>3 Using…

A: the given function,  f(x)=-x+22+1,x≤-2x+1,-2≤x≤3x-32-1,x>3

Q: 9 Determine the domain of the function f(x) 5 - Domain (in interval notation):

A: Solve for the domain

Q: Determine an expression for f(x) in which f(x) is a quartic function, f(x) > 0 when -2 1,f(x) has a…

A: The given function has double root when x=3 The concavity changes at -2 and 1. therefore,…

Q: Identify the open intervals on which the function is increasing or decreasing. (Enter your answers…

A: Given: y=x36-x2 To Find: To identify the open intervals on which the given function is increasing or…

Q: What are even and odd functions of symmetry? For example f(-x)=-f(x), f(-x)=f(x), Symmetric about…

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Q: Find the domain of the function. Give your result in interval notation. f(x)=7/1-2e^x

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Q: Consider the function f(x) = square root of (x + 4 - 2) for the domain [-4, infinity). Find f-1(x),…

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Q: find continuity of the following function on its domain: f(x) = Root of x^2-4

A: The given function is  f(x)=x2-4

Q: State whether the function f has an inverse. If f-1 exists, find the rule for f-(x show that…

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Q: Please illustrate the difference between a function being continuous and differentiable by…

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Q: determine algebraically whether the function is odd, even, or neither f(x) = -x -3x3+ sinx

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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.