Question: REAL ANALYSIS: 6. Fix a E R and define the function f by f(x) = |x - a| for x E R. Prove that f

REAL ANALYSIS:

6. Fix a E R and define the function f by f(x) = |x - a| for x E R. Prove that f is not differentiable at a.2. Let f be a real-valued function defined on R. Let S C R be nonempty and bounded above, and let f(S) = {f(x) : x E S}. Suppose that f is increasing on R and that f is continuous at sup S. Prove that f(S) is bounded above and that sup f(S) = f(sup S')

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