Question

$f\left(x\right)=\{\begin{array}{c}{x}^{2}ifxisirrational\\ 1ifxisrational\end{array}$, then

• A. f(x) is continuous for all x
• B. discontinuous for all x except at x = 0
• C. discontinuous for all x except at x = 1 or -1
• D. none of these

Answer 1

The correct option is C discontinuous for all x except at x = 1 or -1

$f\left(x\right)=\{\begin{array}{c}{x}^2,x\in rational\\ 1,x\in rational\end{array}$

Clearly discontinuous for all $x$ except $-1$ and $1$