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

Solution.

$$f(x,y,z)=\frac{x}{2y-3z}, x,y,z \in Z.$$

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

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

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

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