Answer
Statement is true
Work Step by Step
We are given that the domain of $f(y,x )$ is on the xy-plane; we have to comment about the domain of $f\left(\sin ^{-1} t, \sqrt{t}\right)$
So, we know that domain of $\sin ^{-1} t$ is on [-1,1]. And $\sqrt{t}$ is defined for $t \geq 0$. So, the domain of $f\left(\sin ^{-1} t, \sqrt{t}\right)$ will be [0,1] because for [-1,0), $\sqrt{t}$ can't be defined. The statement is true.
