Question

If $f\left(x\right)=\{\begin{array}{cc}\left[x\right],& -2\le x\le -\frac{1}{2}\\ 2x^2-1,& -\frac{1}{2}<x\le 2\end{array};$ where $[.]$ represents the greatest integer function, then the number of point(s) of discontinuity of $f\left(x\right)$ is

• A. $1$
• B. continuous at every point in domain
• C. $2$
• D. $3$

Answer 1

The correct option is C $2$

$f\left(x\right)=\{\begin{array}{cc}\left[x\right],& -2\le x\le -\frac{1}{2}\\ 2x^2-1,& -\frac{1}{2}<x\le 2\end{array}$
$\Rightarrow f\left(x\right)=\{\begin{array}{cc}-2,& -2\le x<-1\\ -1,& -1\le x\le -\frac{1}{2}\\ 2x^2-1,& -\frac{1}{2}<x\le 2\end{array}$


From graph it is clear that function is discontinuous at $x=-1,-\frac{1}{2}$ in the given domain.