Let ƒ(x) = (ax + b )/(cx + d ), c ≠ 0, ad - bc ≠ 0. a. Give a convincing argument that ƒ is one-to-one. b. Find a formula for the inverse of f.

Q: Find a, b, and c for the function f(x) = a sin(bx − c) such that the graph of f matches the figure.

A: Given Graph of y=asin(bx-c)   To find a , b and c

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: Use the product rule to differentiate the function h, where a and b are real numbers. h(x) = e¯ax…

A: According to product rule, if f(x)=u(x)*v*x) then f’(x)=u(x)*v’(x)+v(x)*u(x).

Q: Let f(x)= x2 − 6. Prove that the root of this function is equal to √6 {correct to 2 dp}, and lays…

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Q: Let f(x) = x², g(x) = 2ª, and h(x) = sin x.

A: Solve by using trigonometric ratio

Q: Use the Chain rule to differentiate each function (a) f(x) = In(x +sin(x)) b) g(x) = (-2x² +3x + 1)3…

A: Chain rule is used to determine the derivative of the composite functions. Consider a composite…

Q: At the point shown on the function above, which of the following is true? Of' > 0, f'' > 0 Of' > 0,…

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Q: In the given question, explain why Rolle’s Theorem does not apply to the function even though there…

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Q: Let f(x) = x², g(x) = 2" , and h(x) = sin x.

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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: Let f: [1,1]→ R be a function given by f(x)=2x-x2. Then the inverse image (preimage) of [0,4] under…

A: The answer is option D

Q: Determine the status of the function f(x) x² + 1'* € (-0, co0). strictly increasing O

A: NOTE: Refresh your page if you can't see any equations. . take derivative

Q: For the function f(x) =-X find f"(X), f"(0), f’"(1), and f"(- 1). "(X) = O I7

A:

Q: Use Part I of the Fundamental Theorem of Calculus to find each of the following when f(x) = | t*dt…

A: By using Part I of the Fundamental Theorem of Calculus:f'(x)=x4

Q: Find the inverse of each function and state its domain. π π a. f(x) = sin(2x) for -< x < 4 4 b. f(x)…

A: Part(a): Given function is, fx=sin2x for -π4≤x≤π4 Let the given function as, y=sin2x Now, solve the…

Q: The domain of the function f(x)= tanh( - 23) is (A, 264)

A: Given,          The domain of the function fx=tanh-1xk-23 is A,264.

Q: Find F as a function of x and evaluate it at x = 0, x = /3, and x = = Tt/2. F(x) 6 de

A: We will use basic formula of Integration for first one and from second part just Value of the…

Q: Find all the points in the interval [1, 5] for f (x) x + 6x – 6 such that the function verifies the…

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Q: We can find an analytic function f=u+vi such that 2u-3v+1 is not harmonic. False True

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Q: Suppose that f"x) = *> 0, f'(1) = -1, and f(e) = 3. Find f(e*). %3D %3D %3D

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Q: Find the function f(x), such that f(x)= In(3x) J ƒ(1)=1.

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Q: Exercise 3.5. For each of the following functions determine the inverse image of T = {r €R : 0S ? –…

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Q: Tell whether the following functions are linearly independent or linearly dependent, and prove your…

A: Linearly Independent: Set consisting of vectors x1 ,x2 , x3.......xn is said to be L.I. if…

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

A: To find the derivative using fundamental theorem of calculus.

Q: the function f (2) = z Cos z ̟has a zero of order

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Q: Let h(x)=f(x)/g(x). If f(x)=−cos(x) and g(x)=4x2+2x−3, what is h′(x)?

A: If f(x)=−cos(x) and g(x)=4x2+2x−3, what is h′(x)?

Q: Use the second fundamental theorem of calculus to evaluate the following: x, x 20 10. [* f(x) dx if…

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Q: Find F as a function of x and evaluate it at x = 0, x = 1/3, and x = T/2. F(x) = cos e de F(x) =…

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Q: Show that f is strictly monotonic on the given interval and therefore has an inverse function on…

A: Show that f is strictly monotonic on the given interval and therefore has an inverse function on…

Q: Find inverse F(S)= F(s)= 3(5*14) an %3D

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Q: Find F as a function of x and evaluate it at x = 2, x = 5, and x = 8.

A: Integral formula:∫xndx = ∫xn+1n+1.dx  + c

Q: If f is a positive function and f"(x) < 0 for a < xs b, show that T, < f(x) dx < M,

A: f is a positive function and f''(x)&lt;0 for a≤x≤b This tells us that f is concave down over the…

Q: Two runners start a race at the same time and finish in a tie after 5 minutes. Prove that at some…

A: Suppose gt and  ht be the positions of the first and second runners at the time t respectively.…

Q: use THE INVERSE FUNCTION RULE TO FIND 1. FOR FACH or THE Fou OWING : (dY 本 y

A: Here we have to find out dy/dx.

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: Let f(x)={tan(2x) ax+b if x>0 if x<0 For which values of a and b is f(x) differentiable for every…

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Q: Express the function F(x) g(x) = ||||| ✓cosa in the form fo g.

A: To express the function Fx=cos x in the form f∘g.

Q: Express the function in the form  f ° g   F(x ) = cos x2

A: Given that, F(x) = cos (x^2) Let us consider, f(x) = cos x g(x) = x^2

Q: consider the ff. function: f(x, y) = cot" "^ (1+x) - 2x + ³y 3y 2e

A: Given the function             f(x, y)=cot-1(1+x)-2ex+3y Where              x=s2+t2,  and…

Q: Use Part I of the Fundamental Theorem of Calculus to find each of the following when f(x) t6 dt.…

A:

Q: Determine the approximate value of one of the roots of the function f(x) = x3 – x + 1 by applying…

A: Given  The function is f(x) = x3-x+1 .

Q: Find a function ƒ and a real number a such that e+ S(t) dt = r*e".

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Q: Prove that the identity function is differentiable at every x E R

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Q: Find F as a function of x and evaluate it at x = 2, x = 4, and x 8. X. F(x) 2 dt

A: First we solve the integration and after that  We put the value of x in the solved part.

Q: If f is a function satisfying |f (x) – f(y)| < (x – y)? - for all x and y, prove that f is constant.

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Q: the function f(x) = xe-* is concave upward on Select one: O (-00, 2) O (2, co0) O (-00, 1) O (1, 0)…

A: Given

Q: Let f' : N → R be a function defined as f'(x) = 4x2+ 12x + 15. Show thatf : N→ S, where, S is the…

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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: