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## Homework Statement

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

## Homework Equations

I know a function is continuous if lim x-->c f(x) = f(c)

## The Attempt at a Solution

I have no idea how to even start this question. I know a function is continuous on an open interval if it is continuous for all interior points, but how do I even begin to show that? Please help?!