Question 286185
Reminder: The domain is the set of all allowable inputs. You can think of this as the set of all possible 'x' values (that produce some number as an output).


Remember that you CANNOT divide by zero. So if the denominator {{{2-3x=0}}}, then {{{x=2/3}}} (solve for 'x'). This means that if {{{x=2/3}}}, then {{{2-3x=0}}}.



In other words, if {{{x=2/3}}}, then the denominator is zero (which is not allowed). So we must exclude this value from the domain. Since there are no other values that make the denominator zero, this means that the only value to exclude from the domain is {{{x=2/3}}}



So the domain is the set of all real numbers except {{{x<>2/3}}}



We denote this in interval notation as  *[Tex \LARGE \left(-\infty,\frac{2}{3}\right)\cup\left(\frac{2}{3},\infty\right)]



Basically, this is the interval *[Tex \LARGE \left(-\infty,\infty\right)] with the number {{{2/3}}} taken out of it.