You visited us 1 times! Enjoying our articles? Unlock Full Access!

Continuity of a Function

If sgn x de...

Question

If $s g n (x)$ denotes signum function then, no. of points of discontinuities of $f (x) = s g n (x^{3} - x)$ is discontinuous at x =

3

Right on! Give the BNAT exam to get a 100% scholarship for BYJUS courses

1

No worries! We‘ve got your back. Try BYJU‘S free classes today!

0

No worries! We‘ve got your back. Try BYJU‘S free classes today!

2

No worries! We‘ve got your back. Try BYJU‘S free classes today!

Open in App

Solution

The correct option is C $3$
$s g n (x^{3} - x) = \frac{∣ ∣ x^{3} - x ∣ ∣}{x^{3} - x}$

$s g n (x^{3} - x) = - 1$ if $x^{3} - x < 0$
$= 0$ if $x^{3} - x = 0$
$= 1$ if $x^{3} - x > 0$

So, the function is discontinuous at those points where $x^{3} - x = 0$

$x^{3} - x = 0$

$x (x^{2} - 1) = 0$

$x (x + 1) (x - 1) = 0$

$x = 0, 1, - 1$

Suggest Corrections

Similar questions

f (x) = min {x^{2}, - x + 1, s g n | - x |}

f (x)

sgn (x)

x

f (x) = s g n (cos 5 x)

x \in (0, π), n, m \in I

m

If [.] denotes greatest integer function, then at which of the following points $f (x) = [x] sin (\frac{π}{2} ([x] + x))$ is discontinuous?

f (x) = {\begin{matrix} | x | - 3, & x < 1 | x - 2 | + a, & x \geq 1 \end{matrix}

g (x) = {\begin{matrix} 2 - | x |, & x < 2 sgn (x) - b, & x \geq 2 \end{matrix}

sgn (x)

h (x) = f (x) + g (x)

a

b

f (x) = {\begin{matrix} [cos π x], & 0 \leq x \leq 1 | x - 1 | [x - 2], & 1 < x \leq 2 \end{matrix}

([.]

)

Join BYJU'S Learning Program