Question

Which one of the following graph of the function are continuous interval $[-1,1]$

• A. $f\left(x\right)=\left\{\begin{array}{c}-x^{2}if-1\le x<0\\ x^{2}if0\le x\le 1\end{array}\right\}$
  
• B. $f\left(x\right)=\left\{\begin{array}{c}1if-1\le x<0\\ \frac{1}{x}ifx=0\end{array}\right\}$
• C. both A and B
• D. none of these

Answer 1

The correct option is A $f\left(x\right)=\left\{\begin{array}{c}-x^{2}if-1\le x<0\\ x^{2}if0\le x\le 1\end{array}\right\}$

$\underset{x\to 0^{+}}{lim}f\left(x\right)$

$=\underset{x\to 0^{+}}{lim}{x}^2$
$=0$

$\underset{x\to 0^{-}}{lim}f\left(x\right)$

$=\underset{x\to 0^{-}}{lim}-x^2$
$=0$
Hence

$LHL=RHL$ at 0.

Hence the function is continuous in the interval $[-1,1]$.