Find the inverse function of f informally. Rx) = x³ + 5 Verify that f( x)) = x and f(f(x)) = X. =x and f(f(x)) = x. F(F=!(x)) 3

Q: Show that the function f (x) = 1- x is bijective and also find (i) its inverse function.

A: Bijective Function :  A function is said to be bijective or bijection, if a function f: A → B…

Q: Let g(x) = 7-X. Find the derivative of the function g. g'(x) =-In 7 %3D

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Q: Verify Rolle's theorem for the function f(x) = 2x2 – 20x + 33 on the interval [2, 8]. -

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Q: Let f(x) = V5x + 4. Compute (f-1)'(2) using the Derivative of an Inverse Function Theorem.

A: Solution

Q: Prove that the function f(x) = x 5 + 2x 3 + 4x − 12 cannot have two real roots. (Hint: Use the first…

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Q: Differentiate the function. f(x) =  3x 2  - 2 cos x

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Q: Z→ Z be such that f(x) = 4x + 2. Is f invertible, and if so, find its inverse function.

A: Given query is to find the inverse function.

Q: Differentiate the function.      f(x)  =        ______1______                            In x

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Q: Give a characteristic that the two functions f(x)=x and g(x) = 2' have in common.

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Q: Differentiate f(x) = a4x4 -3ax² with respect to x. Assume that a is a constant. f'(x) =

A: f(x)=ax4-3ax2 differentiate with respect to x

Q: When we introduced the quotient rule, we didn't actually prove it. Let's do that using only the…

A: Given Data: Function: fxgx=fx·gx-1   The chain rule for derivative is, ddtfgt=f'gtg't ......1   The…

Q: Differentiate  f and find the domain of f f(x)  =    ln ln ln x

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Q: Find the derivative of the following function g2 F(x) = ds a 3+ 5s4 using the appropriate form of…

A: Given that,

Q: Show analytically that the function f is not differentiable at x = x² x1

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Q: Prove that for all a, b = R, the function f(x) = 3x² - 4x³ + 6x² + ax + b has exactly one point…

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Q: Prove that 1 3V2 dx < 3 + x (Hint: Theorem 5.9(ii) and carefully chosen functions should do the…

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Q: Which of the following represents the derivative of f at x? f'(x) = f(x₁-Ax) + f(x1) Ax f'(x) =…

A: See this solution

Q: Differentiate the function In x f(x) = In 2x +3, x>0

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Q: D. Discuss the continuity of the function g (x): 1 %3D on the interval [-1,2]. x2-4

A: Given, To discuss continuity of the function g(x)

Q: Find (f-)'(a). f(x) = 4 + x2 + tan(Tx/2), -1 < x < 1, a = 4 %3D (F-1)'(a) =

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Q: The function f(x)=(2-x)/(3) is continuous at

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Q: Consider the function f(x) = (5x2 +9)(5x² – 9). (a) Compute the derivative of f(x) by multiplying…

A: As we know that the Power law: ddxxn=nxn-1 The product rule: f·g'=f'·g+f·g'   From the given…

Q: Let f(x) = 4x^2 – 7x. Use the ɛ/8-definition of the derivative to prove that f'(2) = 9.

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Q: +1 Differentiate the function f (x) = In +1

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Q: Let f be a function defined by f(x) = ln(3 − 2x). What is the maclaurin function expression of the…

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Q: Compute f(-4) for the function f defined below. x <0 f(x) = 1x2 - 9, x20 %3D

A: Given Function : f(x)=6xx&lt;0x2-9x≥0

Q: Find the linearization of the function at a . f(x) = sin x    , a = pie /6

A: The given function fx=sinx, a=π6

Q: 3 Show that the function f(x) = Vx – 5 is one to one function. %3D

A: The objectives to show that the function f(x) is one to one function.

Q: u² -v² +uv x=In", y=' (11–v)-

A: two functions x=lnuv...........(i) and y=u2-v2+uv(u-v)2..........(ii) are given. To find the…

Q: 20. Express the function F(x) = 1/x + J three functions. X as a composition of

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Q: How to use the standard y = f(x) notation to indicate that (a, b) is an element of the function f?

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Q: Determine the domain of the function f(x) = In(ln r) + x

A: f(x) = ln(ln x) + x f(x) is not defined if ln x &lt;= 0 [as then ln(ln x) is not defined] ln x &lt;=…

Q: Determine where the function F(x)=8x/x2+4 is continuous. The function is continuous on ?

A: Suppose   are continuous function at then rational function is continuous at   if .

Q: Prove that f (x) = x2 takes on the value 0.5 in the interval [0, 1].

A: Here given

Q: Differentiate the function. h(x) = In(x + V - 12

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Q: 24, Find the domain of H function fw =J 2x+3 -1

A: Given,

Q: Show that if f(x) is a non-negative, increasing concavefunction, then ln [ f(x)] is also a concave…

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Q: Show that the function g(x) =x |x | has an inflection point at (0,0) but  g " (0)  does not exist.

A: Given function:                                 g(x)=x|x|   To find out the Inflection point=?…

Q: Differentiate the function. g(x) = In(xe-Sx)

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Q: Let f(x) = ∥x∥. Find out its conjugate function f ⋆ and prove your conclusion.

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Q: Find the linearization L(x)of the function at a .

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Q: Assume that f(x) is a differentiable and invertible function so that f(3) = 4 and f'(3) = .…

A: fx is differentiable and invertible function so that f(3)=4 and f'(3)=12

Q: 6. Prove that the function f defined by f (x)= ,xe(-00,1), has an inverse function 1-x defined on…

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Q: Is the function f(z) = (x2 - y2) + 2xyi entire? Why or why not?

A:

Q: Decide whether or not the real function In (cos 2x) 2x2 x + 0, f(x) = -1, = 0, x = is continuous at…

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

Q: Let h(x) = 8(x) f(x) If f (x) = cos (x) and g(x) = 4x² + 2x – 3, what is h' (x)?

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

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Q: Evaluate the derivative of the inverse function of f at the given value c) f(x) = Vx² + 4 find…

A: Givenf(x)=x2+43

Counting Principles

In statistics, the counting principle can be said to be the concept in which the quantity of an item is determined. There can be a single item, or a group of items, or items that are related to each other. In every possible set of items, the quantity of the possible item groups or their sorting measures can be determined with counting principles.