A function f(x) is said to have a removable discontinuity at x=a if:
1. f is either not defined or not continuous at x=a.
2. f(a) could either be defined or redefined so that the new function IS continuous at x=a.

Let f(x)=x−22x2+4x−16
Show that f(x) has a removable discontinuity at x=2 and determine what value for f(2) would make f(x) continuous at x=2.
Must define f(2)=?

Question

A function f(x) is said to have a removable discontinuity at x=a if: 
1. f is either not defined or not continuous at x=a. 
2. f(a) could either be defined or redefined so that the new function IS continuous at x=a.

Let f(x)=x−22x2+4x−16 
Show that f(x) has a removable discontinuity at x=2 and determine what value for f(2) would make f(x) continuous at x=2. 
Must define f(2)=?

anonymous · Answer

Got it, it is 12.
factor 2 first , then (x-2) then get the limit of f(2) by plugging 2 into the final function which is 2(x+4) and that will give you 12