Question

find the domain of the function expressed by the formulay= 2/3 +xpls write the answer as a equation

Answer 1

The function is

$y=\frac{2}{3+x}$

Remember that, for y to be a number, we cannot have things of the form

$\begin{gathered} \frac{1}{0},\frac{2}{0},\ldots \\ \frac{1}{0},\frac{2}{0},\ldots\notin\mathfrak{\Re } \end{gathered}$

Therefore, we always need to avoid this kind of result.

We can see that the only way 'y' acquires a value like that is if

$\begin{gathered} 3+x=0 \\ \Rightarrow x=-3 \end{gathered}$

Therefore, y is well for any value of x, except when x=-3.

Thus, the domain of the function y (y(x)) is

$x\in(-\infty,-3)\cup(-3,\infty)=\mathfrak{\Re }-\mleft\lbrace-3\mright\rbrace$

The domain of y is all the numbers except for -3