Let g be the inverse of (x) = x 3 + 1. Find a formula for g(x)

Question:

Let g be the inverse of ƒ(x) = x³ + 1. Find a formula for g(x) and calculate g'(x) in two ways: using Theorem 2 and then by direct calculation

THEOREM 2 Derivative of the Inverse Assume that f is differentiable and one-to- one with inverse g(x) = f(x).

Fantastic news! We've Found the answer you've been seeking!

Step by Step Answer:

Related Book For answer-question

Calculus

ISBN: 9781319055844

4th Edition

Authors: Jon Rogawski, Colin Adams, Robert Franzosa

See More Books

Question Posted: Dec 01, 2023 03:15 AM

See More Questions

In Problems 1-4, find the convergence set for the given power series. Find a formula for the nth term; then use the Absolute Ratio Test? 1. x / 1 ( 2 - x2 / 2 ( 3 + x3 / 3 ( 4 - x4 / 4 ( 5 + x5 / 5 (...
Carter, Inc. produces two different products, Product A and Product B. Carter uses a traditional volume-based costing system in which direct labor hours are the allocation base. Carter is considering...
Let E = {(x, y): 0 < y < x} and set f(x, y) = (x + y, xy) for (x, y) E. a) Prove that f is 1-1 from E onto {(s, t): s > 2t, t > 0} and find a formula for f-1[ (s, t). b) Use the Inverse Function...
Write a reflective paper about Disability Network West Michigan
Avicorp has a $10 million debt issue outstanding, with a 6% coupon rate. The debt has semi-annual coupons, the next coupon is due in six months, and the debt matures in five years. It is currently...
Dave has $100,000 to invest in 10 mutual fund alternatives with the following restrictions. For diversification, no more than $25,000 can be invested in any one fund. If a fund is chosen for...
Determine the number of ideal stages required in Example 7.4 if the solvent rate used is twice the minimum. Data From Example 7.4:- A solution of acetic acid (C) in water (A) is to be extracted using...
Mark Corporation estimates its manufacturing overhead to be $90,000 and its direct labor costs to be $200,000 for year 1. The actual direct labor costs were $50,000 for Job 301, $75,000 for Job 302,...
Assistant please, 1) Discuss two impacts to the Database management process by the Data definition language (DDL) and Data manipulation language (DML). 2) Share with a business partner two...
Consider the logistic world population model from Example 2: (a) Determine the time t when the population is half of the expected long-term limit of 17.4 billion. (b) There is a single point of...
Refer to the appropriate triangle or trigonometric identity to compute the given value. tan (sec 1 (2))
Use the Chain Rule to show that if is measured in degrees, then d/d (sin ) = / 180 cos (This gives one reason for the convention that radian measure is always used when dealing with trigonometric...
Softcore Consultancy Services is in the IT sector. It is currently facing a shortage of skilled labor and is experiencing an increase in employee salaries, which has been increasing over the past few...
What are the potential applications of motivation research in optimizing educational practices, workplace dynamics, and interventions aimed at promoting health behavior change?
How can technological advancements be leveraged to democratize access to resources and enhance empowerment on a global scale?
Find an example of policymaking in the health sector at the US federal level and answer the following questions: a) How is the policy-making process demonstrated in your example? b) What components...
How does one reconcile ethical principles with the complexities of modern decision-making in a globalized economy ?
Fill in the blanks in the following separate income statement through a identify any negative amount by putting it in parentheses Particulars 60.000! S 42,500| S 36,000| S 45,600 S 23,600 Sales Cost...
Fahrad Inc. sells all of its product on account. Fahrad has the following accounts receivable payment experience: Percent paid in the month of sale .........10 Percent paid in the month after the...
The area A of a triangle whose base is b and whose altitude is h is A = _______ .
List the intercepts and test for symmetry: x 2 + y = 9.
True or False The point (1, 2) is on the line 2x + y = 4.
1. What is the definition of diversity in its broadest terms in ways other than simply race or ethnicity? 2. Assess the roles of culture and diversity in stakeholders and other constituents...
1. Convert into Normal-Form Game and Find out the subgame-Nash Equi- libria? Entrant OUT IN Entrant (0,2) Small Large Incumbent Small Large Small Large (-6, -6) (-1,1) (1,-1) (3, 3) 2. What does the...
What role do change agents and champions play in driving change management efforts, and how can their leadership skills and influence be harnessed to catalyze organizational transformation?

Let g be the inverse of (x) = x 3 + 1. Find a formula for g(x)

Question:

THEOREM 2 Derivative of the Inverse Assume that f is differentiable and one-to- one with inverse g(x) = f(x). If b belongs to the domain of g and f'(g(b)) #0, then g'(b) exists and g'(b)= = 1 f'(g(b)) 3

Step by Step Answer:

To find gx we solve y x 1 for x Therefore the ...View the full answer

Calculus

Students also viewed these Mathematics questions