Question

Number of points of discontinuity of $f\left(x\right)=[2x^3-5]$ in $[1,2)$, is equal to-(where $\left[x\right]$ denotes greatest integer less than or equal to $x$)

• A. $14$
• B. $13$
• C. $10$
• D. $8$

Answer 1

The correct option is A $14$

$f\left(x\right)=[2x^3-5]$ in $[1,2)$ is discontinuous and $[.]$ is G.I.F.

We know that $x^3$ is continuous $\Rightarrow 2x^3-5$ is also continuous.

Now, range of $2x^3-5$ for $xϵ[1,2)$ will be

$-3\le 2x^3-5<11$

$\Rightarrow (2x^3-5)ϵ[-3,11)$

We know G.I.F is discontinuous at integers, $f\left(x\right)$ is also a G.I.F. with domain as $[-3,11)$, so $f\left(x\right)$ will be discontinuous at integer in $[-3,11)$

$\Rightarrow$No. point of discontinuity=no. of integers in $[-3,11)$

$=14$