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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