How do I determine whether a function is bounded?

1 Answer
Reginaldo D.
Oct 27, 2014

A function f is bounded in a subset U of its domain if there exist constants M, m in RR such that

m<=f(x)<=M, for all x in U.

For example,

  1. f(x)=sin(x) is bounded in RR because

-1<=sin(x)<=1, for all x in RR.
2. f(x)=x^2 is bounded in [0,1] because

0<=x^2<=1, for all x in [0,1].

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