What can you conclude about the inverses of functions whose graphs are lines perpendicular to the line y = x?

Q: Explain why every nonconstant linear function has an inverse.

A: Given: A linear function has an inverse.

Q: How would you define an inverse function in your own words? Please write as short as possible 

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Q: What is the common way to obtain a new function from an existing one?

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Q: 2х-9 F(x)% = %3D 4х

A: We have to find the definition of the derivative to find f(x). By the definition of the derivative,…

Q: Suppose that x and y vary inversley and that Y=8/3 when x=8. Write a function that models the…

A: Given that x and y vary inversely that is  y=kx where k is proportionality constant.

Q: can an even function be selv-inverse?an odd function?

A: Can an even function be self-inverse?an odd function?

Q: Use the derivative to explain why the function f(x) = x³ + x³ is a one to one %3D function.

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Q: Use the graph of f to draw the graph of its inverse function.

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Q: Find the exact location of the relative and absolute extrema of the function.

A: Solve the following

Q: What is the slope of the line tangent to the graph of a function defined by f(x)= x² + √x at x=1?

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Q: When functions are defined by more than one equation,they are called________ functions.

A: When functions are defined by more than one equation,they are called________ functions.

Q: Find the equation of the line tangent to the graph of f at the indicated value of x. f(x) = 6 + In…

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Q: In your own words explain how to form the composition of two functions.

A: Query- In your own words explain how to form the composition of two functions. Answer- Camposition…

Q: List the points in the graph at which the function is not differentiable.

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Q: What rule should be used in getting the derivative of a.)  f(x) = x^5 b.) h(x) = 3(x + 4)^3 c.)…

A: a. fx=x5 The rule used to get the derivative of given function is, ddxxn=nxn-1 The derivative is,…

Q: Find the equation of the line tangent to the graph of f at the indicated value of x. f(x)=3-2lnx;…

A: To determine equation of tangent line at given point.

Q: What is the derivative of f(x)= f(x)=(x^5-x^3-x)/x^3

A: f(x)=x5-x3-xx3   To find: f'(x)

Q: Sketch the graphs of two distinct functions with the property f′(x)=−x^2+x

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Q: Find the derivative of the function. F(x) = (3x5 + 4x3)4 F'(x) =

A: Given, F(x)=3x6+4x34 To find F'(x).

Q: When functions are defined by more than one equation,they are called ___________________ functions.

A: When functions are defined by more than one equation, they are called ___________________ functions.

Q: Sketch the graph of the derivative for function shown.

A: Plot the derivative for -∞<x<0. The function f(x) is constant in the interval -∞<x<0 so…

Q: How does your relationship with someone special related to the one-to-one and inverse function?

A: We will try and understand one one functions and inverse functions using the relations around…

Q: Use a computer algebra system to find the derivative of the function.

A: g(x)=x+1x+22x-5

Q: -10

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Q: Find the derivative of the function. f (x) = (x 4  + 3 x2  - 2) 5

A: The given function is f (x) = (x 4  + 3 x2  - 2) 5

Q: Find the derivative of the function. F(x)=x^3-6/x^2+5

A: GivenFx=x3-6x2+5We have to find the derivative of the function .Rule apply :-Quotient rule…

Q: Find the derivative of the function. F(x) = (5x6 + 8x³)4 F'(x) =

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Q: When examining the formula of a function that is the result of multiple transformations, how can you…

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Q: Find the derivative of the function. f(x) = 9x2 (x − 6)

A: We have to find the derivative of the function

Q: If I reverse a function’s components, will this new relation be a function?

A: Suppose a function f(x)=3x+5 with the input of x and gives the result y.

Q: Can this be a one to one function?

A: Defnition:  Let f:R→R be a function , if f is said to be one to one then every element in domain has…

Q: How can the One-to-One Functions Graphically be identified?

A: If a function has no two ordered pairs with different first coordinates and the same second…

Q: Use the definition of the derivative to differentiate each function. 5) f(x) = x' - 16 6) f(x) = x°…

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

Q: How can we Represent a Function Numerically?

A: A function f from a set A to a set B is a rule that associates every member of set A a unique member…

Q: If f(x) = (2x) , find the derivative of the function Or) = f'(x) = 3(x)0.5 f'(x) = -(x)0.5 f'(x) =…

A: 1)f(x)=(2x) -0.5 2)f(x)=(1+sinx)/(x+cosx).

Q: How can a graphing utility be used to visually determine if two functions are inverses of each…

A: Consider the given information as  Graphing utility be used to visually determine if two functions…

Q: How are the graphs of a function and its inverse are closely related?

A: The function f(x) and g(x) are the inverses of each other if it satisfies the identity…

Q: State the domain of the function and the domain of the derivative. f(x)= 6/2x^2 f'(x)= Domain of…

A: We find f'(x) using the power rule

Q: Use the definition of the derivative to differentiate each function. 1) f(x) = x° - 10x² + 32x - 32…

A: 1. fx=x3-10x2+32x-32 Using the definition of derivative: f'x0=lim△x→0△y△x=lim△x→0fx0+△x-fx0△x Now,…

Q: What is the Horizontal Line Test for One-to-One Functions?

A: we have to define the horizontal line test for One-to-One Functions.

Q: The original and restricted functions are not the same functions.True or false?

A: Given, 'The original and restricted functions are not the same functions.

Q: What is the relationship between the graph of a function and the graphof its inverse?

A: Consider the function fx and inverse of f(x) is represented by f-1x.

Q: Why do we restrict the domain of a function when we are finding the inverse? *

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Q: Find the derivative of the function. f(x) = 10/((x ^ 2 - 4) ^ 4)

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Q: Find the inverse of the function on the given domain f(x) = 3x2 + 5, (-∞, 0)

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Differential Equations

Have you ever observed the movement of the satellites and rockets or how the planets go around the sun in their orbits? How will you determine their motion? Definitely they follow some scientific laws and these kinds of problems are framed as differential equations.