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)= x2+10x+26 2 −x2−10x−24 if x−5 if x=−5 if x−5
Show that f(x) has a removable discontinuity at x=−5 and determine what value for f(−5) would make f(x) continuous at x=−5.
question:
Must redefine f(−5)=

Answer 1

A function with a removable discontinuity could be redefined to remove the discontinuity if, at the point of removable discontinuity (x=-5) in this case, Lim f(x) x->-5^- and x->-5⁺ are equal.

The discontinuity can be removed by redefining f(x) such that f(-5)=one of the above limits.

As I am unable to read unambiguously the definition of the function f(x), I am not able to show that f(-5) should be.