6. A function f : R → R is said to be bounded if |f(x)| M, for some M > 0. Give an example of function f: R → R that is bounded and an example of such function that is unbounded. Also, give an example of function where sup{f(x) : x € R} €R but max{f(x) : x E R} does not exist.

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6.
A function f : R → R is said to be bounded if |f(x)| M, for some M > 0. Give
an example of function f: R → R that is bounded and an example of such function that is
unbounded. Also, give an example of function where sup{f(x) : x E R} € R but max{f(x) : x €
R} does not exist.
Transcribed Image Text:6. A function f : R → R is said to be bounded if |f(x)| M, for some M > 0. Give an example of function f: R → R that is bounded and an example of such function that is unbounded. Also, give an example of function where sup{f(x) : x E R} € R but max{f(x) : x € R} does not exist.
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