Question: The function f: X Y has an inverse function f -1: Y X if and only if f is one-to-one and onto.

The function f: X → Y has an inverse function f -1: Y → X if and only if f is one-to-one and onto.

Step by Step Solution

★★★★★

3.25 Rating (154 Votes )

There are 3 Steps involved in it

1 Expert Approved Answer
Step: 1 Unlock

Assume is onetoone and onto Then for every there ex... View full answer

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

Document Format (1 attachment)

Word file Icon

914-M-N-A-O (379).docx

120 KBs Word File

Students Have Also Explored These Related Numerical Analysis Questions!

Q:

The function f(x) = k(2 x x3) has an inverse function, and f1(3) = 2. Find k.

Q:

The controls {f-1(y): y Y} of a function f: X Y partition the domain X. For any particular y Y, its pre image f -1(y) may be Empty Consist of a single element Consist of many elements Where f...

Q:

f: X Y is continuous if and only if f (x) limn f(xn) for every sequence xn x. Care must be taken to distinguish between continuous and open mappings. A function f: X Y is continuous if f-1(T) is...

Q:

The function f (x) = (x-5)"+2 is not one-to-one. Identify a restricted domain that makes the function one-to-one, and find the inverse function. (1 point) O restricted domain: x 2 5; f-1(x) =5- ~x-2...

Q:

Using your knowledge of inverses complete table for the inverse of the function f x 2 Graph the inverse function on the same axes Label each graph appropriately as f x and f x Answer the following...

Q:

sir i am stuck for this question Question 11 (0.14 points) Use Taylor's polynomial of degree 2 of the function f(x) = tan-1(x-1) + x2 about c = 1 to estimate the value of f (0.7). Enter a decimal...

Q:

Please answer all if possible thanks. 4. Define the following sets (30 points) (a) X = {(x, y) R 2 : y = f(x) = 3x + 3y 42} (b) Y = {(x, y) R 2 : y = f(x) = 2x + 2y 42} (c) Z = X Y (d) Prove whether...

Q:

Find the inverse of the function f x x 5 The inverse function of f x x 5 is f x 165465 2010 2018 ALDE LE BUR CONSER DEPRESS Il es CERVE Gestal PAR 1000 S MEREN SELINS PRYLAR

Q:

The set of integers is the domain and the codomain for the following function. Select one of the following choices to describe this function f ( x ) = 2 x + 1 a.)f is both one to one and onto b.)f is...

Q:

In Problems 5162, the function f is one-to-one. (a) Find its inverse function f 1 and check your answer. (b) Find the domain and the range of f and f 1 . (c) Graph f, f 1 , and y = x on the same...

Q:

The following data represents an extract of the final votes, of ten candidates, for an election influenced by previous public service score card of a candidate. Votes 502 685 765 587 728 603 465 625...

Q:

An operation manager of a chemical manufacturing plant must determine the lot size for a chemical that has a steady demand of 1,450 litres per day. The production rate is 6,850 litres per day, setup...

Q:

19. You are the manager of GearNet and must decide how many Internet hubs to produce to maximize your firms profit. GearNet and its only rival (NetWorks) sell dual-speed Internet hubs that are...

Q:

Consider the following LP problem: a) Solve the above LP problem using suitable algorithms. b) Exhibit the optimal primal and dual solutions and the optimal primal and dual bases. c) Verify that the...

Q:

Continuation of Exercise 5-49. Determine the following: (a) Marginal probability distribution of X (b) Conditional probability distribution of Y given X = 1 (c) X(Y|X = 1) (d) P(Y

Q:

The time between surface finish problems in a galvanizing process is exponentially distributed with a mean of 40 hours. A single plant operates three galvanizing lines that are assumed to operate...

Q:

A popular clothing manufacturer receives Internet orders via two different routing systems. The time between orders for each routing system in a typical day is known to be exponentially distributed...

Q:

Elsinore Electronics is a decentralized organization that evaluates divisional management based on measures of divisional contribution margin. Home Audio (Home) Division and Mobile Electronics...

Q:

6. One person found the equation y = 10x + 50 to be a good fit for the 2 points data. Use this model to predict y when x is 9. * Your answer 8. a. Estimate the slope of the line of fit. * 2 points...

Q:

Your company will generate $57,000 in annual revenue each year for the next seven years from a new information database. If the appropriate interest rate is 7.8%, what is the present value of the...