Problem
Find the domain of the following function. If possible, give a description of the domain in words (for example, all points outside a sphere of radius I centered at the origin). \[ f(x, y, z)=4 x y z-2 x z+5 y z \] Find the domain of the function. Select the correct choice below and, if necessary, fill in the answer box to complete your choice. A. $\{(x, y, z): z \leq \square\}$ B. $\{(x, y, z): y \neq \square\}$ (Use a comma to separate answers as needed.) C. $\{(x, y, z): x \neq y, y \neq z, z \neq x\}$ D. $\{(x, y, z): x \geq \square\}$ E. $R^{3}$ Give a description of the domain in words. Select the correct choice below and, if necessary, fill in the answer box to complete your choice. A. All points on or above the plane $x=$ B. All points on the plane $y=$ C. All points not on the plane $y=$ D. All points on or below the plane $z=$ E. All points not on the planes $x=y, y=z$, and $z=x$ F. All points in $\mathrm{R}^{3}$ G. It is not possible to describe the domain in words.
Solution
Step 1 ：The domain of the function is \(\boxed{R^{3}}\). In words, the domain includes \(\boxed{\text{All points in } R^{3}}\).
