Question

Show that the function defined as 𝑓(𝑥) = { 𝑥, 𝑥 ∈ ℚ

𝑥 2 , 𝑥 ∈ ℝ − ℚ

is continuous at 1 and discontinuous at 2.

Accepted Answer

f(x)= \Bigg\{ \begin{matrix} g(x),&x \in Q\ h(x),& x\in \R-Q
\end{matrix}

then funtion f is continuous where g(x)=h(x).

Therefore, we have

x=x^2\ x^2-x=0\ x(x-1)=0\ x=0 ,1

Thus, function f is continuous at x=0,1.

The given function is continuous at x=1 and discontinuous at x=2.

Question #240287

Expert's answer