Q79 / 200 · Manipal (MET) 2013 · Mathematics
- A$x$
- B$x$ except at $x=0$
- Correct answerC$x$ except at $x=1$
- D$x$ excexpt at $x=0$ and $x=1$
Solution
We have; $f(x)=\left\{\begin{array}{cc}\frac{x^2-x}{x^2-x}=1, & \text { if } x \lt 0 \text { or } x\gt1 \\ -\frac{\left(x^2-x\right)}{\left(x^2-x\right)}=-1, & \text { if } 0 \lt x \lt 1 \\ 1, & \text { if } x=0 \\ -1, & \text { if } x=1\end{array}\right.$
$=\left\{\begin{array}{ccc}1, & \text { if } & x \leq 0 \text { or } x\gt1 \\ -1, & \text { if } & 0 \lt x \leq 1\end{array}\right.$
So, $f(x)$ is not continuous at $x=0$. It can be easily seen that it is not continuous at $x=1$ also.
So, $f(x)$ is not continuous at $x=0$. It can be easily seen that it is not continuous at $x=1$ also.
Hence, the correct answer is option: 'C'.