Let $f:\mathbb{R} \rightarrow \mathbb{R}$ be defined as $f(x) = \begin{cases}
x^{2}-1 & x \in \mathbb{Q}\
-x+1& x \notin \mathbb{Q}
\end{cases}$
Prove that $\lim\limits_{x \rightarrow a} f(x)$ exists if and only if $a = -2\ or\ 1$

Question

Let $f:\mathbb{R} \rightarrow \mathbb{R}$ be defined as $f(x) = \begin{cases}
x^{2}-1 & x \in \mathbb{Q}\
-x+1& x \notin \mathbb{Q}
\end{cases}$
Prove that $\lim\limits_{x \rightarrow a} f(x)$ exists if and only if $a = -2\ or\  1$

dan815 · Answer

what is Q?

ganeshie8 · Answer

rationals

dan815 · Answer

okay so since -x+1, x not a member of rationals

dan815 · Answer

u have to show that the irration numbers around -2 converge to 2

dan815 · Answer

converbe to 3*

dan815 · Answer

and show that irrational numbers around 1 aswell first then we can see why no other numbers shud work

dan815 · Answer

look at the intersection of these 2 functions

dan815 · Answer

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