Proof a function is continuous

[Dr. Science]

Homework Statement

Suppose that a function f has the property that

|f(x) - f(t)| < or = |x-t| for each pair of points in the interval (a,b). Prove that f is continuous
on (a,b)

Homework Equations

?

The Attempt at a Solution

f(x) and f(t) must be defined everywhere on (a,b)

 

[Mark44]

Homework Statement

Suppose that a function f has the property that

|f(x) - f(t)| < or = |x-t| for each pair of points in the interval (a,b). Prove that f is continuous
on (a,b)

Homework Equations

?

The Attempt at a Solution

f(x) and f(t) must be defined everywhere on (a,b)

By "prove" do you mean an epsilon-delta proof?

 

[Dr. Science]

i have no idea, that's all the question says. it just says to prove f is continuous

 

[Mark44]

What's the definition of continuity at a point?

 

[Dr. Science]

as x approaches c f(x) = f(c)

 

[╔(σ_σ)╝]

Write down a more precise definition and then pick epsilon appropriately; make it slightly greater than delta. :-)