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## Homework Statement

part 1)Show the function a(x)=|x| is a continuous function from R to R;

part 2)

Prove that if the functions f: D--> R is continuous at x=a, then l f l (absolute value of f) is also continuous at x=a.

## Homework Equations

## The Attempt at a Solution

part 1) since a(x) = |x|, then given any [tex]\epsilon[/tex] > 0, then for all l f(x) - f(a) l < [tex]\epsilon[/tex], since l x - a l < [tex]\delta[/tex] when delta = epsilon, since f(x) = l x l

part 2) since f is continuous, then the absolute value of f is also continuous since it doesnt change any of the relationships

then given any [tex]\epsilon[/tex] > 0, then for all l f(x) - f(a) l < [tex]\epsilon[/tex], since l x - a l < [tex]\delta[/tex] when delta = epsilon, since f(x) = l x l