Question

$f:(0,\infty )\to (-\frac{\pi }{2},\frac{\pi }{2})$ be defined as, $f\left(x\right)=arctan\left(lnx\right)$

On the basis of above information, answer the following questions :

If $s_1,x_{2}and{x}_3$ are the points at which $g\left(x\right)=\left[f\right(x\left)\right]$ is discontinuous where [.] denotes greatest integer function, then $x_1+x_2+x_3$ is

• A. Equal to 2
• B. Equal to 3
• C. Greater than 3
• D. Greater then 2 but less than 3

Answer 1

Answer: (C)

Greater than 3

From graph, g(x) is discontinuous at $x=x_1,x_2,x_3$

${\tan }^{-1}\left(\ln x_1\right)=-1;{\tan }^{-1}\left(\ln x_2\right)=0;{\tan }^{-1}\left(ln{x}_3\right)=1$
$\Rightarrow x_1=\frac{1}{e^{\tan 1}};x_2=1;x_3=e^{tan1}$
$\therefore x_1+x_2+x_3=e^{\tan 1}+\frac{1}{e^{\tan 1}}+1>3.$