How should f(2) be defined so that f is continuous on (0, ∞) ?

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1 Answer
Monzur R.
Apr 2, 2018

#f# is not continuous on #(0,oo)# no matter how we define #f(2)#.

Explanation:

A function is continuous at a point #x=c# if three things are satisfied:

  • #f(c)# is well-defined
  • #lim_(x->c)f(x)# exists
  • #lim_(x->c)f(x)=f(x)#

For this particular #f#, the second bullet point is not satisfied so #f# can never be continuous at #x=2#.

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