Question about strictly increasing

[nikefish]

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

 

[SammyS]

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 ?

.

 

[HallsofIvy]

The first thing you should do is graph the function.

 

[klondike]

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