Function f(x) = l , , ,x - 1, ;x < 2 2x - 3, ,x 2 . is a continuo… - Vidyadip

MCQ

Function $f(x) = \left\{ \begin{array}{l}\,\,\,x - 1,\;x < 2\\2x - 3,\,x \ge 2\end{array} \right.$ is a continuous function

✓
For all real values of $x$
B
For $x = 2$ only
C
For all real values of $x$ such that $x \ne 2$
D
For all integral values of $x$ only

✓

Answer

Correct option: A.

For all real values of $x$

a
(a) Since $\mathop {\lim }\limits_{x \to 2 - } f(x) = \mathop {\lim }\limits_{x \to 2 + } f(x) = f(2) = 1$

Also it is continuous for all values of $x$, less than $2$ and greater than $2$.

Need a full question paper?

Generate a complete, print-ready paper with questions like this in minutes — across 16+ boards, with answer keys.

Start Generating Free

Explore more

More "M.C.Q (1 Marks)" from 5. continuity and differentiation→5. continuity and differentiation — all question types→Maths STD 12 Science question papers→Gujarat Board STD 12 Science question papers→Gujarat Board question paper generator→

Similar questions

What will be the volume of that parallelopiped whose sides are $ a = i -j + k, b = i -3j + 4k $ and $c = 2i -5j + 3k$ ................ $\mathrm{unit}$

The function $\text{f(x)}=\begin{cases}\frac{\sin3\text{x}}{\text{x}},&\text{x}\ne0\\\frac{\text{k}}{2},&\text{x}=0\end{cases}$ is continuous at x = 0, then k =

3
6
9
12

If $y = {e^x}\log x$, then ${{dy} \over {dx}}$ is

A coin is tossed $2n$ times. The chance that the number of times one gets head is not equal to the number of times one gets tail is

The area bounded by the curve y = x⁴ - 2x³ + x² + 3 with x-axis and ordinates corresponding to the minima of y is:

$1$
$\frac{91}{30}$
$\frac{30}{9}$
$4$

$\left| {\,\begin{array}{*{20}{c}}a&b&c\\b&c&a\\c&a&b\end{array}\,} \right| = $

The function $f(x) = 2ln\,|x| -x|x|$ is increasing on the interval

The number of real solutions of $x^{7}+5 x^{3}+3 x+1=$ $0$ is equal to............

If lines $\frac{x-1}{-3}=\frac{y-2}{2 k}=\frac{z-3}{2}$ and $\frac{x-1}{3 k}=\frac{y-5}{1}$ $=\frac{z-6}{-5}$ are mutually perpendicular, then $k$ is equal to

${d \over {dx}}\left( {{{\tan }^{ - 1}}\sqrt {{{1 + \cos {x \over 2}} \over {1 - \cos {x \over 2}}}} } \right)$ is equal to