#### Answer

$f(x,y,z)$ is continuous for value $y \geq x^2$ and $z \gt 0$

#### Work Step by Step

As we are given that $f(x,y,z)=\sqrt {y-x^2} \ln z$
The function $f(x,y,z)=\sqrt {y-x^2} \ln z$ represents a represents a squared root function which cannot be less than $0$.
Thus,
$ \sqrt {y-x^2} \geq 0$
or, $y \geq x^2 $
and $\ln z \gt 0$
or $z \gt 0$
This means that $ y \geq x^2 ; z \gt 0$
Hence, $f(x,y,z)$ is continuous for value $y \geq x^2$ and $z \gt 0$