Question

Determine the domain of this relation {(x,y):y=((3/x)-5}

Answer 1

Given relation:

$\mleft\lbrace(x\text{ , y}\mright)\to\text{ y = }\frac{3}{x}\text{ - 5}\}$

The domain is the set of allowable x values

Re-arranging the function representing the relation:

$\begin{gathered} y\text{ = }\frac{3}{x}\text{ - 5} \\ =\text{ }\frac{3-5x}{x} \end{gathered}$

When we equate the denominator to zero, the function becomes undefined.

Hence, the domain of the relation using interval notation is:

$(-\infty\text{ , 0) }\cup\text{ (0 , }\infty\text{ )}$