Let the given graph is of y = f(x)
Then $\mathit{f}\left(-\frac{\mathit{\pi }}{2}\right)=0=\mathit{f}\left(\frac{\mathit{\pi }}{2}\right)$
Therefore, we need to choose an interval such that the function is one - one.
One such interval is [0, π]
$\Rightarrow$ The range of f(x) will be domain of ${\mathit{f}}^{-1}\left(\mathit{x}\right)$ and vice-versa.
Also, the ${\mathit{f}}^{-1}\left(\mathit{x}\right)$ is image of f(x)
About y = x line
${\mathit{f}}^{-1}\left(\mathit{x}\right)$ domain will be [-1, 1] and range will be [0, π], option (C) satisfy the criteria.