I was thinking about the following problem:
Consider the function $f:\mathbb R \rightarrow \mathbb R$ defined by $\begin{align}f(x) &=\begin{cases} x^{4} \,\,\,\,\,\,\,\,\,\,\,\,\text{if x is rational} \\ 2x^{2}-1 \,\text{if x is irrational}\end{cases}\end{align}$ . Let $S$ be the set of points where $f$ is continuous. Then which of the following is correct?
(a) $S=\{1\}$
(b) $S=\{-1\}$
(c) $S=\{-1,1\}$
(d) $S=\phi$.
Can someone point me in the right direction? Please help.Thanks in advance for your time.