Answer:
[tex](-\infty,-\frac{2}{5})\cup(-\frac{2}{5},\infty)[/tex]Explanation:
Given the function:
[tex]f(x)=\frac{5x-9}{5x+2}[/tex]We are required to find the domain of the given function.
The domain of a rational function are the set of values of x for which the denominator is not equal to 0.
To find the domain of f(x), set the denominator equal to 0 to find the excluded values.
[tex]\begin{gathered} 5x+2=0 \\ 5x=-2 \\ x=-\frac{2}{5} \end{gathered}[/tex]The excluded value in the domain of f(x) is -2/5.
Therefore, the domain of f(x) in interval notation is:
[tex](-\infty,-\frac{2}{5})\cup(-\frac{2}{5},\infty)[/tex]