Choose the correct answers from the given four options: The funct… - Vidyadip

MCQ

Choose the correct answers from the given four options:
The function $\text{f(x)}=\frac{4-\text{x}^2}{4\text{x}-\text{x}^3}$ is:

A
Discontinuous at only one point.
B
Discontinuous at exactly two points.
✓
Discontinuous at exactly three points.
D
None of these.

✓

Answer

Correct option: C.

Discontinuous at exactly three points.

We have, $\text{f(x)}=\frac{4-\text{x}^2}{4\text{x}-\text{x}^3}=\frac{(4-\text{x}^2)}{\text{x}(4-\text{x}^2)}$

$=\frac{(4-\text{x}^2)}{\text{x}(2^2-\text{x}^2)}=\frac{4-\text{x}^2}{\text{x}(2+\text{x})(2-\text{x})}$

Clearly, f(x) is discontinuous at exactly three points x = 0, x = -2 and x = 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 CONTINUITY AND DIFFERENTIABILITY→CONTINUITY AND DIFFERENTIABILITY — all question types→Maths STD 12 Science question papers→Gujarat Board STD 12 Science question papers→Gujarat Board question paper generator→

Similar questions

Let $E ^{ C }$ denote the complement of an event $E$. Let $E _{1}, E _{2}$ and $E _{3}$ be any pairwise independent events with $P \left( E _{1}\right) > 0$ and $P \left( E _{1} \cap E _{2} \cap E _{3}\right)=0$ Then $P \left( E _{2}^{ C } \cap E _{3}^{ C } / E _{1}\right)$ is equal to

There are $6$ boxes labelled $B_1, B_2, \ldots, B_6$. In each trial, two fair dice $D_1, D_2$ are thrown. If $D_1$ shows $j$ and $D_2$ shows $k$, then $j$ balls are put into the box $B_k$. After $n$ trials, what is the probability that $B_1$ contains at most one ball ?

The general solution of the differential equation $\frac{\text{dy}}{\text{dx}}+\text{y}\ \text{g}(\text{x})=\text{g}(\text{x})\ \text{g}'(\text{x})$ is a given function of x, is:

$\int_{ - 1}^1 {|1 - x|dx} = $

The equation of motion of a stone, thrown vertically upwards is $s = ut - 6.3{t^2},$ where the units of $s $ and $t $ are $cm$ and $sec.$ If the stone reaches at maximum height in $3$ sec, then $u =$ ......... $cm/\sec $

$\int_0^a {\frac{{x\,dx}}{{\sqrt {{a^2} + {x^2}} }}} = $

Matrices $\mathrm{A}$ and $\mathrm{B}$ will be inverse of each other only if

If ${\sin ^{ - 1}}x + {\sin ^{ - 1}}y + {\sin ^{ - 1}}z = \frac{{3\pi }}{2}$, then the value of ${x^{100}} + {y^{100}} + {z^{100}} - \frac{9}{{{x^{101}} + {y^{101}} + {z^{101}}}}$ is equal to

From which of the following the distance of the point $(1,\,\,2,\,\,3)$ is $\sqrt {10} $

Let $f$ be function such that $f(x + y) = f(x) + f(y)$ for all $x$ and $y$ and $f(x) = (2x^2 + 3x)g(x)$ for all $x$; where $g(x)$ is continuous and $g(0) = 3.$ Then $f '(x)$ is equal to :-