Consider the function : f ( x ) = [ x ] + | 1 - x |, , - 1 x 3 wh… - Vidyadip

MCQ

Consider the function :

$f\left( x \right) = \left[ x \right] + \left| {1 - x} \right|,\, - 1 \le x \le 3$ where $[x]$ is the greatest integer function

Statement $1$ :$f$ is not continuous at $x = 0, 1, 2$ and $3$

Statement $2$ :$f\left( x \right) = \left( \begin{array}{l}
- x,\,\,\,\,\,\,\,\,\, - 1 \le x < 0\\
1 - x,\,\,\,\,\,\,\,0 \le x < 1\\
1 + x,\,\,\,\,\,\,\,1 \le x < 2\,\\
2 + x,\,\,\,\,\,\,2 \le x \le 3
\end{array} \right.$

✓
Statement $1$ is true ; Statement $2$ is false,
B
Statement $1$ is true; Statement $2$ is true;Statement $2$ is not correct explanation for Statement $1$
C
Statement $1$ is true; Statement $2$ is true;Statement It is a correct explanation for Statement $1$.
D
Statement $1$ is false; Statement $2$ is true

✓

Answer

Correct option: A.

Statement $1$ is true ; Statement $2$ is false,

a
Let $f\left( x \right) = \left[ x \right] + \left| {1 - x} \right|, - 1 \le x \le 3$

where $[x]=$ greatest integer function.

$f$ is not continous at $x=0,1,2,3$

But in statement - $2$ $f(x)$ is continuous at $x=3$.

Hence, statement - $1$ is true and $2$ is false.

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