Question

The domain of the given function in interval notation is ____f(x) = 5x - 9 —————- 5x + 2

Answer 1

`(-\infty,-(2)/(5))\cup(-(2)/(5),\infty)`

Explanation:

Given the function:

`f(x)=(5x-9)/(5x+2)`

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.

`\begin{gathered} 5x+2=0 \\ 5x=-2 \\ x=-(2)/(5) \end{gathered}`

The excluded value in the domain of f(x) is -2/5.

Therefore, the domain of f(x) in interval notation is:

`(-\infty,-(2)/(5))\cup(-(2)/(5),\infty)`