Mathematics - Inverse Trigonometric Functions Question with Solution | TestHub

Within the real domains, the equation is ${\mathrm{x}}^2+\mathrm{x}+1=\lambda \mathrm{x}+1$, giving $\mathrm{x}=0$ or $\mathrm{x}=\lambda -1$. At the second root the ${\sin }^{-1}$ domain requires $-1\le x\le 0$, and distinctness requires $x<0$, hence $0\le \lambda <1$. The only listed integer is $\lambda =0$.