The function f(x) = l x + 2 , , , ,, , , ,1 x 2 4 , , , , , , , ,… - Vidyadip

MCQ

The function $f(x) = \left\{ \begin{array}{l}x + 2\,\,\,\,,\,\,\,1 \le x \le 2\\4\,\,\,\,\,\,\,\,\,\,\,,\,\,\,x = 2\\3x - 2\,\,,\,\,\,x > 2\end{array} \right.$ is continuous at

A
$x = 2$ only
B
$x \le 2$
C
$x \ge 2$
D
None of these

✓

Answer

Clearly the function is defined only in the interval $[1,\infty ]$
hence option $(b)$ cannot even apply.
For $x > 2,y = 3x - 2$ which is a straight line, hence continuous.
Further $y = 4$ at $x = 2$.
Hence, the function is continuous at $x = 2$ also $($but not at $x = 2$ only $).$

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