Question

Problem 5. Let \( f(x)=m x+b \) be a linear function on \( \mathbb{R} \). Show \[ |f(x)-f(y)|=|m||x-y| \] for all \( x, y \in \mathbb{R} \). Thus linear functions are Lipschitz on all of \( \mathbb{R} \).

          Problem 5. Let \( f(x)=m x+b \) be a linear function on \( \mathbb{R} \). Show
\[
|f(x)-f(y)|=|m||x-y|
\]
for all \( x, y \in \mathbb{R} \). Thus linear functions are Lipschitz on all of \( \mathbb{R} \).

Problem 5. Let f(x)=m x+b be a linear function on ℝ. Show

|f(x)-f(y)|=|m||x-y|

for all x, y ∈ℝ. Thus linear functions are Lipschitz on all of ℝ.

Added by Cassie M.

Calculus

Dale Varberg, Edwin Purcell deceased,… 9th Edition

Chapter 3

Instant Answer

Solved by Expert Likhit Ganedi

Step 1

Step 1: Start with the given linear function \( f(x) = mx + b \). Show more…

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Problem 5. Let \( f(x)=m x+b \) be a linear function on \( \mathbb{R} \). Show \[ |f(x)-f(y)|=|m||x-y| \] for all \( x, y \in \mathbb{R} \). Thus linear functions are Lipschitz on all of \( \mathbb{R} \).