Question

The number of solutions of the equation $\left[si{n}^{-1}x\right]=-\left[x\right]$ is (where [*] denotes the greatest integer function)

• A. 0
• B. 1
• C. 2
• D. infinitely many

Answer 1

The correct option is D infinitely many

$\left[{\sin }^{-1}x\right]=0,x\in [0,\sin 1]$

$\left[{\sin }^{-1}x\right]=1,x\in [\sin 1,\pi /2]$

$\left[{\sin }^{-1}x\right]=-1,x\in [-\sin 1,0]$

$\left[{\sin }^{-1}x\right]=-2,x\in [-\pi /2,-\sin 1]$

$-\left[x\right]=0,x\in [0,1]$

For $x\in [0,\sin 1]$ , both LHS & RHS are zero

$\Rightarrow$ infinite solution