Question: Let A, B C R, let a E A and let f : A - B is a bijection. Suppose f is differ- entiable at

Let A, B C R, let a E A and let f : A - B is a bijection. Suppose f is differ- entiable at a such that f'(a) * 0. Prove using the definition of differentiation that the inverse function f-is differentiable at the point b = f(a) and ( f- 1 ) (b) = f' (a)

Step by Step Solution

There are 3 Steps involved in it

1 Expert Approved Answer

Step: 1 Unlock blur-text-image

Question Has Been Solved by an Expert!

Get step-by-step solutions from verified subject matter experts

Step: 2 Unlock

Step: 3 Unlock

Students Have Also Explored These Related Law Questions!

Let a, b E R and r E E41 Consider a circle centred at (a, b) with radius r. We lmow the solutions to the equation (a: a): + {y ii}? = 1'2 describes the circle. (a) Give mo differentiable flmctions f,...

Exercise 5.3.2. [Used in Exercise 5.5.6.] Let [a, b] C R be a non-degenerate closed bounded interval, and let f: [a, b] - R be a function. Suppose that f is integrable. Prove that if If(x) |

Give Correct ANSWERS Human-Computer Interaction (a) If you had been one of the original inventors of the WIMP interface, and engineers on the technical team had been sceptical about the advantages...

Portray in words what transforms you would have to make to your execution to some degree (a) to accomplish this and remark on the benefits and detriments of this thought.You are approached to compose...

ccn2 java solve them all . . . r2 e1 e2 box r2 Write sound typing and subtyping rules for these constructs. [5 marks] Now suppose that we add to this calculus the type variables and bounded universal...

ccm1 java attend all . . . r2 e1 e2 box r2 Write sound typing and subtyping rules for these constructs. [5 marks] Now suppose that we add to this calculus the type variables and bounded universal...

Trusted software could then be run on the workstation. Discuss the advisability of this approach to workstation design. (10 marks) b) Explain how distributed inter-process communication (IPC) is...

Suppose that R(A, B, C) is a relational schema with functional dependencies F = {A, B C, C B}. (i) Is this schema in 3NF? Explain. [2 marks] (ii) Is this schema in BCNF? Explain. [2 marks] (b)...

Department of Computer Science & Software Engineering Comp232 Mathematics for Computer Science Winter 2017 Assignment 3. Due date: March 30, by 23:59 EDT 1. For each of the following, determine...

Subaru Motors Corporation (SMC) today announced plans to revise its organisational structure. The changes will see the company's structure slim down from 230 departments to 131, which will hopefully...

Find and view several online videos on recent cyberattacks (less than 2 years ago). Identify the URLs for 2 videos that you think do a particularly good job of illustrating (1) the worst-case...

-24/35 (-16/25) Perform the indicated operation by hand.

Prepare Baker Ltd s Statement of Cash Flows for the year ended 3 1 March 2 0 2 5 using the indirect method in accordance with IAS 7 : Statement of Cash Flows. Show all workings clearly and reference...

Coxner Industries Berhad has an expected Earnings Before Interest and Taxes (EBIT) of $420,000 in perpetuity and a tax rate of 35 percent. The firm has $70,000 in outstanding debt at an interest rate...