Question: prove that the function is bijective f : ( 0 , 1 ) R defined as f ( x ) = x ( 1 x

prove that the function is bijective

f:(0,1)R

defined as f(x)=x(1x)12x

(explain in detail every step)

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 Mathematics Questions!

Q:

Help is appreciated, thank you! Recall that the indicator function of rationals is not Riemann integrable. Prove directly (by constructing appropriate partitions) that the function f given below is...

Q:

(a) Consider the function f : R - R defined by 2 if x 0. (i) Prove that f is discontinuous at 0. [3] (ii) Using only the definition of continuity, prove that f is continuous at every c 0. [5] (b)...

Q:

Give an example of a function f which satisfies the intermediate-value property on a closed and bounded interval [a, b] but is not continuous on a, 6). () Give an example of a function f which is...

Q:

Functional analysis Questions 81 17:35 Expert Q&A W + 3. Prove that the metric space ( of all bounded scalar sequences is complete. Recall that the metric on 2 is given by doo (x, y) = sup | - Vil,...

Q:

This is Analysis. Please prove every part clearly. a domain D in R. Problem 4. Write the definition and the negation of the definition of uniform continuity for a function f on (i) Prove that if f is...

Q:

In this project you will construct an increasing function that is discontinuous at each rational point in (0, 1) and continuous at each irrational point in (0, 1). We will need two basic facts: a....

Q:

Math 125 A: Homework 5 Due Thursday, November 9 1. For n = 1, 2, let fn : E R and suppose that fn f uniformly for some function f . Show that if each fn is bounded, then f is bounded. 2. Let {fn } be...

Q:

How to solve these 3 different questions? ( 2 marks ) Consider the function f : R > IR defined by an) = 4a: +8taII1 at. First let us evaluate f(1) (in the exact form). f(1)= -42*Pi o n E . Let us...

Q:

CS 70 Discrete Mathematics and Probability Theory Fall 2015 Jean Walrand HW 13 1. Statistical hypothesis testing On one of the Mythbusters episodes1 , the Mythbusters decided to run an experiment to...

Q:

Let f : R" -> R be a twice differentiable function with a positive semidefinite hessian. For any two points r, y ( R", we will show that the one-dimensional function g : [0, 1] -+ R defined as g(t)...

Q:

Between -0.62 and 1.78. Assume that a randomly selected subject is given a bone density test. Those test scores are normally distributed with a mean of 0 and a standard deviation of 1. In each case,...

Q:

Find the equation of the line pasing through (2, -1, 2) and (5, 3, 4) and of the plane passing through (2, 0, 3), (1, 1, 5) and (3, 2, 4). Also, find their point of intersection.

Q:

Tyrell Company issued callable bonds with a par value of 5 0 0 0 0 The call option requires Tyrell to pay a call premium of 5 0 0 plus par or a total of 5 0 5 0 0 to bondh

Q:

Stafford Company prepared a static budget for a production and sales volume of 10,000 units. Per unit standards Static Budget $ 10,000 $650,000 $65.00 $11.00 $ 9.00 $ 4.20 110,000 90,000 42,000...