5. Let f(x) = x³ +x – 1. It turns out that f(x) is an invertible function (you don't need to prove this) and its inverse is denoted as f-'(x). (a) By trial and error, find a value r such that f(x) = -3. (b) What is the value of f-1(-3)? (c) Calculate the value of (f-1)'(-3), the derivative of f-1 at x = -3. Note: f-1(x) and (f-1)'() are too difficult to find; you are not asked to find those functions. You are ONLY asked for the value of (f-1)'(-3).

Q: 1. Find the general form of f if f'(x) = 4(x).

A: We have to find the general form of the function f if f'x=4 fx. Rewriting the given equation, f'x=4…

Q: Evaluate f''(c) at the point. f(x) = (x2 - 4)(x3- 2), c = 1

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Q: 1 If y = V1-x then y' = 2/1-x

A:

Q: f(x) = x2 +9 Find all the values of x for which f' (x) = 0. What is the product of all these values?…

A: To find the values of x such that f'(x)=0 see below the calculation

Q: 3x + 1 Consider the function f(x) Compute each of the following. Simplify your answer and use x - 3…

A: Given f(x)=-3x+1x-3

Q: 2. Determine f'(1) for the function f(x) = (8x – 6Vx5 + 3) (x² – 9x² +) -

A: A detailed solution is given below

Q: 3) Let f(x)= 2x+3 . Calculate by definition f'(2).

A:

Q: If f(z) = (3z -3)(2-22), use the product rule to find f'(0). %3D

A:

Q: The function f(x)=(x)/(x-1) is discontinous at x=1 because

A:

Q: Find f'(x) and simplify. X X-19 f(x) = Which of the following shows the correct application of the…

A: Given that       f(x) = x/(x-19)

Q: The inverse of the function f(x) = +3 is f-'(x) =. O 5(x – 6) 25(x – 3) O 35(x – 3) O 10(x – 3) 5(г…

A: We will find the inverse function as following.

Q: QUESTION 2 Find the general solution, in terms of real functions only, of x' = 3x + 4y y' = -0.5x +…

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Q: 3x+1 Evaluate f'(-1) given that f(x) = %3D 2x+1

A:

Q: e +1 Differentiate the function f(x)= In 5x +1 Se+1 3ex+1 Sesz e3x +1 ,5x +1 e 3e3z Sesz e3x +1 5x…

A:

Q: Determine whether the functionf is one-to-one by examining the sign of f' (x). (a)ƒ(x) = x³ + 9x2 –…

A:

Q: Find the following using the table below. X 1 2 3 4 3 4 f(x) 2 1 f'(x) 2 4 3 1 g(x) 2 4 3 1 g'(x) 2…

A: 1) given function h(x)=f(x).g(x)Derivative w.r.t 'x' by using the product ruleformula of the product…

Q: Provide the table of signs for both f' and ff'.

A: Given function is fx = x+334x-12 = x4 +12x-1+16x-12 +114. Also, given that f'x = x-9x+324x-13    and…

Q: the inverse function of f(x) = ax is x+c hat is the value of a + b + c? +C= f-¹(x)= 8x - 7 .-x+3'

A: Topic:- algebra and calculus

Q: f(x) = In (1+x³)

A:

Q: Let f. g:1 R be differentiable functions on I and c e I with g'(c) # 0. Then lim f(x) (e) %3D e g(x)…

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Q: Let F(x) = f(f(x)) and G(x) = (F(x))² and suppose that f(9) = 13, f(13) = 3, f'(13)=9, f'(9) = 7…

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Q: 3-5x 11. Find f'(x), if (i) f (x) = (x² – 1)(x5 + 2)+/3, and (ii) f (x) (x3+2)1/3*

A:

Q: Suppose Im(f(z)) = 6x(2y -1) and f(0)= 3 -2i, f(1) = 6- 5i. Find f(1 + i)

A: Complex function

Q: Suppose f(x) and g(x) are two functions such that: • f(3)=1 • g(3)=1 • f(3)=5 • g'(3)=7 What is…

A: we know that uv' = u'v+v'u                   product chain rule of differentiation

Q: 4x + 3 Find the inverse of f(x) 1 ƒ-'(x) =

A:

Q: The inverse of function f(x) = x3 + 2 is а) f-1 (y) %3 (у - 2) 1/2 b) f-1 (y) = (y – 2) 1/3 c) f-1…

A:

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.