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Question about strictly increasing

  • Thread starter nikefish
  • Start date
  • #1
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Homework Statement


Hello, Does anybody know how to solve this question? Or a formal way to prove that a fuction is strictly increasing?

Define f(x)={ x-1 if x<0
x+1 if x >_ 0

Show that f: R -> R is strictly increasing and that f^(-1) : f(R) -> R is continuous at 1


Homework Equations





The Attempt at a Solution

 

Answers and Replies

  • #2
SammyS
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Homework Statement


Hello, Does anybody know how to solve this question? Or a formal way to prove that a fuction is strictly increasing?

Define f(x)={ x-1 if x<0
x+1 if x >_ 0

Show that f: R -> R is strictly increasing and that f^(-1) : f(R) -> R is continuous at 1

Homework Equations



The Attempt at a Solution

Hello nikefish. Welcome to PF !

What have you tried ?

Where are you stuck ?



What is your definition of a strictly increasing function ?

.
 
  • #3
HallsofIvy
Science Advisor
Homework Helper
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The first thing you should do is graph the function.
 
  • #4
125
2
Use the definition of "strictly increasing" to show part 1 and use the definition of "continuous" for part 2.

Homework Statement


Hello, Does anybody know how to solve this question? Or a formal way to prove that a fuction is strictly increasing?

Define f(x)={ x-1 if x<0
x+1 if x >_ 0

Show that f: R -> R is strictly increasing and that f^(-1) : f(R) -> R is continuous at 1


Homework Equations





The Attempt at a Solution

 

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