## 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

## The Attempt at a Solution

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SammyS
Staff Emeritus
Homework Helper
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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

## 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
Homework Helper
The first thing you should do is graph the function.

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