Question

Find the domain and range of the function f, defined by :

f(x,y,z) = x/(2y-3z) : x,y,z∈ R

Answer 1

For this function one condition must hold: the denominator cannot be zero. Since

$$2y-3z \neq 0, \newline 2y\neq 3z, \newline y\neq 1.5z.$$

Domain(f)=$\{(x,y,z) \in R^3|y\neq 1.5z\}.$

Range (f)=R (all real numbers).