Mathematics - Inverse Trigonometric Functions Question with Solution | TestHub

For $\mathrm{a}>0$, the curves cross between $\mathrm{x}=0$ and $\mathrm{x}=\sqrt{\mathrm{a}}$ or elsewhere by continuity. For $\mathrm{a}\le 0$, the left side is ${\mathrm{x}}^2-\mathrm{a}$ and near 0 the right side is $|x|$. On $[0,\pi ]$, intersection means $x^2-a=x$, so $a=x^2-x$ has minimum $-1/4$ at $x=1/2$. Thus exactly $\mathrm{a}\ge -1/4$ works, selecting A, B, D.