a)Find the inverse of f(x)=x+1. Graph ?and its inverse together. Add the line ?=?on the same sketch. b)Find the inverse of f(x)=x+b, where ?is constant. How is the graph of f−1related to the graph f. c)What can you conclude about the inverses of functions whose graphs are lines parallel to the line y=x.

Q: 05:- Find the inverse function f-1(x) if exists in the following cases:- c) f(x) = 1-

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Q: Consider the function f(x) = 2x2+1. Find the equation of the tangent to the graph of f(x) at x = 2.…

A: Not sure why we need to calculate f inverse of 2. We do need to calculate the value of the…

Q: The derivative to determine whether the function is strictly monotonic on its entire domain and…

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Q: (2.4) Determine the equation that defines the inverse function f-1. (2.5) Show that (fof-1) (x) = X…

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Q: The derivative to determine whether the function is strictly monotonic on its entire domain and…

A: We have given fx=1-x3-6x5 By differentiating the function, f'x=-3x2-30x4=-3x21-10x2 Now, we find the…

Q: Find the slope of the tangent line to the graph of the function at the given point. g(x) = 19 – x²;…

A: The given data is: gx=19-x2 To find the slope of the tangent line at the point 3,10.

Q: (a) Find the inverse function of f(x) = 2x - 3. f-¹(x) = (b) The graphs of f and f are symmetric…

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Q: 4. Let a be a real number such that 0 < a < 1, and let f(t) = eat – t where t e R. a) Find the…

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Q: (a) Find the inverse function of f(x) = 4x – 4. f (x) +1 1 (b) The graphs of f and f are symmetric…

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Q: Illustrate that the functions are inverse functions of each other by sketching their graphs on the…

A: Sketch the graph of functions fx=ex-1   and  gx=lnx+1 on the same set of coordinate axes as shown…

Q: For function, find (a) the equation of the secant line through the points where x has the given…

A: Given : fx=-3x+1 ; x=1, x=5 To find : a) the equation of the secant line through the points where x…

Q: The graph of f', the derivative of f, is shown. On the same coordinate plane, sketch a possible…

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Q: (a) Find the inverse function of f(x) = 2x – 7. f-l(x) = 1 (b) The graphs of f and f are symmetric…

A: Using definition of inverse function,

Q: Find f′(x) and find the equation of the line tangent to the graph of f at the indicated value of x.…

A: Given a function 'f' of x and find its first derivative . And also find at x=1 tengent line equation…

Q: 9. Determine the coordinates of a point(s) that do not change between the original and the…

A: Given that: f(x)=-x2+5

Q: 4. a) If you were given a function in the form y = g(x), explain how you would determine the…

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Q: The derivative to determine whether the function is strictly monotonic on its entire domain and…

A: Givenf(x)=cos3x2To determine whether the…

Q: (a) Find the inverse function of f(x) = 7x – 8. f-(x) = -1 (b) The graphs of f and fare symmetric…

A: To find the inverse function, swap x and y, and solve the resulting equation for x.

Q: 4 The function f(x) =+5, x# 0, is one-to-one. %3D Find an equation for f '(x), the inverse function.…

A: The given function is: f(x)=4x+5,     x≠0

Q: In the given question , determine whether the statement is true or false. If it is false, explain…

A: To determineTrue or falseslope of the graph of the inverse tangent function is positive for all x.

Q: Illustrate that the functions are inverse functions of each other by sketching their graphs on the…

A: Graph the given functions on the same set of coordinate axes as shown below:

Q: 16. Find the inverse function of f. f(x) = x2 - 3, x 2 0 Then, use compositions of functions to…

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

Q: Suppose that the differentiable function y = g(x) has an inverse and that the graph of g passes…

A: Given,

Q: A) function is defined by f(x) = {²1₂ ² if x20 if x<0 Evaluate f(0), f(1)and f(2) and sketch the…

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Q: Assume that functions f and g are differentiable with f(-3)= -5, f(- 3) = -4, g(-3)=2, and…

A: Equation of a line

Q: Find the equation of the line tangent to the graph of the given function at the point with the…

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Q: For function, find (a) the equation of the secant line through the points where x has the given…

A: Given f(x)=x2+x, x=3, x=6

Q: Let f(x) be a polynomial and g(x) = f '(x) be its derivative. If the degree of (f(x) + f(-x)) is 10,…

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Q: Illustrate that the functions are inverse functions of each other by sketching their graphs on the…

A: y=ln(2-e5x)

Q: Consider the following function. f(x) = x + 4x – 2, (1, 3) (a) Find an equation of the tangent line…

A: Given function is fx=x2+4x-2 and point is (1,3). Differentiating the given function with respect to…

Q: Find the point on the graph of the given function at which the slope of the tangent line is the…

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Q: a. Find the inverse of ƒ(x) = -x + 1. Graph the line y = -x + 1 together with the line y = x. At…

A: PART a.The given function is y = ƒ(x) = -x+1To find the inverse of this function we interchange x…

Q: Find the inverse function (on the given interval, if specified) and graph both ƒ and ƒ-1 on the same…

A: Given: y=fx=x+2; x≥-2 for finding inverse of given function, we find x in terms of y then replace x…

Q: (a) Find the inverse function of f(x) = 6x - 1. f-(2) (b) The graphs of f and f' are symmetric with…

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Q: What is the inverse of a function from A to B under function composition?

A: Let f : A→B be a bijective function.

Q: If f(x) = 4x2 – x³, find f'(x), f"(x), f'(x), and f(4)(x). f'(x) = f"(x) = f""(x) = f(4) (x) = Graph…

A: Given, the function f(x) = 4x2 – x3, then we have to find the f’(x), f’’(x), f’’’(x) and f4(x) and…

Q: 3- Determine two functions g(x) and h(x), neither of which is constant, so that f(x) =f(x) = g(x) 0…

A: The two functions, gx=x2+1x2-1 and hx=x2+1x2+2 such that fx=x2+1x2-1x2+1x2+2. The function is…

Q: Sketch the graph of the function  f(x) = ln∣x∣ and state its domain.

A: Sketch the graph as shown below:

Q: Find an equation for the function f that has the given derivative and whose graph passes through the…

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Q: Consider the following f(x)=1/2x In x^2, (-1,0) Find an equation of the tangent line to the graph…

A: Tangent  line to be find

Q: Let f(x) = 21 – x² The slope of the tangent line to the graph of f(x) || at the point (-4, 5) is The…

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Q: 2 If f(- 4) = – 1, and f'(– 4) = Let f (x) be the inverse function of f(x). (f ')'(- 1) = %3D Write…

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Q: 1 If f(x) has an inverse function f-¹(x), could either the graph of for the graph of f-¹ be…

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Q: If f(x) =2x2 - x3 , find f'(x) , f" (x), f"'(x) , and  f(4) x.Graph f , f' , f" , and f"' on a…

A: Given: f(x)=2x2-x3Differentiating f with respect to x  ⇒…

Q: Assume that functions f and g are differentiable with f(-3)=-3, f'(-3)=5, g(-3)=-4, and g'(-3)=-3.…

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Q: If the function f is a one-to-one function and f -is its inverse function, then if x is in the…

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Q: 1. Sketch the reciprocal of the function f (x) = x - 6.

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Q: of the tangent line to the graph at any point (x,f(x)) is f'(x) and that the graph of f passes…

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Q: Find the slope of the tangent line to its inverse function f^-1 at the indicated point P, and find…

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Q: Find the derivative of the function f(x) = 3x? – - 12x – 28 by definition of derivatives f(x + h) –…

A: A function is a relation which maps each value in its domain to exactly one value in its range. The…

Rate of Change

The relation between two quantities which displays how much greater one quantity is than another is called ratio.

Slope

The change in the vertical distances is known as the rise and the change in the horizontal distances is known as the run. So, the rise divided by run is nothing but a slope value. It is calculated with simple algebraic equations as: