The discussion revolves around proving that a piecewise function is strictly increasing and demonstrating the continuity of its inverse at a specific point. The function is defined as f(x) = x - 1 for x < 0 and f(x) = x + 1 for x ≥ 0.
The discussion is ongoing, with participants seeking clarification on definitions and suggesting methods to explore the problem. Some guidance has been offered regarding the use of definitions for the proof.
There is a repeated request for information on what the original poster has attempted and where they are experiencing difficulties, indicating a focus on understanding the problem rather than providing direct solutions.
Hello nikefish. Welcome to PF !nikefish said: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
nikefish said: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