On the interval I = [- 2, 2], the function f(x) = * 20 c (x , + ,… - Vidyadip

MCQ

On the interval $I = [- 2, 2]$, the function

$f(x) =$ $\left\{ {\begin{array}{*{20}{c}} {(x\, + \,1)\,\,{e^{ - \,\left[ {\tfrac{1}{{|x|}}\,\, + \,\,\tfrac{1}{x}} \right]}}}&{(x\,\, \ne \,\,0)} \\ {0\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,}&{(x\,\, = \,\,0)} \end{array}} \right.$

then which one of the following does not hold good ?

✓
is continuous for all values of $x \in I$
B
is continuous for $x \in I - (0)$
C
assumes all intermediate values from $f(- 2) \& f(2)$
D
has a maximum value equal to $3/e$ .

✓

Answer

Correct option: A.

is continuous for all values of $x \in I$

a
$f (x) =$ $\left[ \begin{gathered} (x + 1){e^{ - 2/x}}\,\,\,\,\,if\,\,\,x > 0 \hfill \\ x + 1\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,if\,\,\,x\, < \,0 \hfill \\ 0\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,if\,\,\,\,x\, = \,0\, \hfill \\ \end{gathered} \right.$

the graph of $f (x)$ is

hence $f$ can assume all values for $f (- 2) to f (2)$

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