Alexander Lorien
New member
- Joined
- Oct 2, 2020
- Messages
- 9
Is the statement, "If ? is a continuous function at a, then so is |?|." true or false? If true, give a formal proof. If false, provide a counterexample.
What is the formal definition of a continuous function?Is the statement, "If ? is a continuous function at a, then so is |?|." true or false? If true, give a formal proof. If false, provide a counterexample.
Do you know that \(||a|-|b||\le|a-b|~?\)Is the statement, "If ? is a continuous function at a, then so is |?|." true or false? If true, give a formal proof. If false, provide a counterexample.
Does it mean that the statement is false? Sorry i am confusedDo you know that \(||a|-|b||\le|a-b|~?\)
\(|a|=|a-b+b|\le|a-b|+|b|\) implies \(|a|-|b|\le|a-b|\)
Likewise \(|b|-|a|\le|b-a|=|a-b|\) or \(-|a-b|\le||a|-|b||\le|a-b|\)
So \(\large\left||a|-|b|\right|\le|a-b|\)
You simply need to sit down with an instructor. You need help.Does it mean that the statement is false? Sorry i am confused
Draw a few functions and see for yourself. You need to see if it is true or not. A few simple drawing will do wonders.Does this mean that the statement is false??