Consider the function
f (x) ={
(x^2 + 10x + 25)/(x + 5) if x != −5,
0 if x = −5.
Is f (x) continuous at the point x = −5? Is f (x) a continuous function on R?

Question

Consider the function
f (x) ={
(x^2 + 10x + 25)/(x + 5) if x != −5,
0 if x = −5.
Is f (x) continuous at the point x = −5? Is f (x) a continuous function on R?

castiel · Answer

I get $$\lim_{x \rightarrow -5}=DNE$$
,
$$\lim_{x \rightarrow -5^{-}}=-infinity$$
and $$\lim_{x \rightarrow -5^{+}}=+infinity$$

I know f(-5)=0 but in order for that function to be continuous it must be $$\lim_{x \rightarrow -5}=f(-5)$$ right? But in the results it says that the funtions is continuous at f(-5) and R?

anonymous · Answer

Sorry, do you mind if I ask you where you got the question from? The first condition for a function to be continuous at a point x is that f(x) is defined, which means x is in the domain of f.

castiel · Answer

I saw my mistake so I closed the question. It was a silly mistake by my part at the beginning. I wrote that (x^2 + 10x + 25)=(x-5)^2 when it's actually (x+5)^2