List all Values of discontinuity

Question

f(x)= {2x-1 if x ≤ -1

         {3x if -1<x<1

         {x+1 if x≥ 1

 

FIND THE VALUES OF DISCONTINUITY FOR THIS FUNCTION . 

 

 

Answer 1

A function ƒ(x) is continuous if the limit of ƒ approaching from BOTH directions exist and if ƒ(x) is a value within the domains.  So you must find where the limit does not exist from one direction and if there is no value within the domain.

 

Therefore:

 

ƒ(x)=x+1 is discontinuous at (-∞,2)

ƒ(x)=3x  is discontinuous  at  (-∞,-1)∪(1,∞)

ƒ(x)=2x-1  is discontinuous at  (-1,∞)