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

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: Consider the function f(x)=2x3+9x2−108x+5,  −6≤x≤4f(x)=2x3+9x2-108x+5,  -6≤x≤4. Use the derivatives…

A: Given, f(x)= 2x³+9x²-108x+5 -6<=x<=4

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: ): Apply Rolle's theorem for the function f(x) = 9x² – 36x + 27 over the interval [1, 3]. Justify…

A: Given :- Apply Rolle's Theorem for the function fx = 9x2 -36x + 27 over the integral 1,3.

Q: Show that the function f(x) = 2x³ – 1, from f: R → R is bijective and find its inverse.

A: The function f(x)=2x3-1, from f:ℝ→ℝ

Q: he domain of the function f(x) = Vx+5 is In(3-x) %3D

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Q: find the derivatives of f(x)= (-3+x^-3)(-4x^3+3) using product rules.

A: We need to find the derivatives of f(x)= (-3+x^-3)(-4x^3+3) using product rules.

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: Find the derivative of the algebraic function. c° - x³, c is a constant. c3 + x3 f(x) = %3D

A: This problem can be solved by using the Quotient rule in derivatives which is explained in step 2.

Q: Determine whether the pair of functions is linearly independent or linearly dependent on the real…

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

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

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Q: Find the derivative of the algebraic functie c3 – x³ c3 + x3 c is a constant. f(x) %3D 6r3 3 (3 +x³)…

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Q: Determine the derivative of a quadratic function of general form y=ax2+bx+c.

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Q: Find the derivatives of the functions in Exercise

A: The derivative of a function is the rate of change of the function with respect to the function…

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

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Q: Use the Second Fundamental Theorem of Calculus to find F '(x).

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Q: Find the derivative of f(x) = (2 - 3x) (-5x + 4). O 2 О 22-30х О зох + 22 30x + O 15x + 8 None of…

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Q: Let f : X → Y be an invertible function. Show that f has unique inverse.

A: Given

Q: Determine whether the functions f1(x) := x + 1; f2(x) := sin(x); f3(x) := x - 1; f4(x) := 3 are…

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Q: Use the second fundamental theorem of calculus to find F'(x)

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Q: Use the Product Rule to find the derivative of the function.

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Q: Let f(æ) = – 3x* In æ %3D f'(x) = f'(e²) =

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Q: Write the first and second derivatives of the function. f(x) = 4.2 In x + 9.3 f'(x) f"(x) %3D

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Q: Apply the definition of the derivative of a function to find f'(x). a. f(x) = 6x + 4 b. f(x) = x2 -…

A: To find the derivative of the function using the definition of the derivative. (a). Given function…

Q: Find a bijective function f : R^+ → R^+ different from the identity function and has the property f…

A: That's easy. Have a great day!!!

Q: Consider a function f(x) = |x – 3|. a. Show that f (x) is not differentiable at 3. -

A: Given         f(x) =|x-3|

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

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

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: Oz(-@) and Ør(@) are conjugate functions. That is, Px(-@) =Øx°(@) %3D and Oz"(-@) = , (@)

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Q: Show that the function f : R−{−2} → R−{1} defined by f(x)=x+1 / x+2 is a bijection, and find the…

A: Topic = Functions

Q: Use the Product Rule to find the derivative of the function. g(x) = (x² – 6x + 7)(x³ – 1) g'(x) =

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Q: Find a function f(x), such that f"(x) = 3sin(4x). %3D

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Q: The function f(x)=/25-x' is contionous on

A: It is continuous function.

Q: Let f (x) = 5x4 + 3x3 + 3x2 + 5x + 5. Fill in the missing coefficients for the derivative of f:

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Q: Determine whether the function f : R\{2} –>R\{0}, defined by f(x)=(1/(x-2)) is bijective or not.

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Q: Find and sketch the domain of the function f (x, y) = In(9 – x² – 9y²).

A: The given function,  f(x,y)=ln9-x2-9y2

Q: Calculate the derivative of the function. g(x) = (x² – 3x – 1)-7 %3D g'(x) =

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Q: Show that f : ℝ → ℝ, f(x) = 5x − 3 is a bijective function.

A: The given function is f:ℝ→ℝ defined by fx=5x-3. We say that a function f is bijective if it is both…

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: 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: Consider z as function of the variables x and y, it is defined by :

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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: Use the Product Rule to find the derivative of the function. g(x) = (x2 − 4x + 2)(x3 − 5)

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

A: The given function is: f(x)=ln xln 2x+3,x>0

Q: Let f(x) = 2x'+3x. Use differentiation from first principles to show that f'(x) = 6x² +3.

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