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question 8
what is the domain of the function (f(x)=\frac{x + 5}{x-9})?
nothing in this list is correct.
((-infty,-5)cup(-5,9)cup(9,infty))
((-infty,-9)cup(-9,infty))
((-infty,-5)cup(-5,infty))
((-infty,5)cup(5,infty))

Explanation:

Step1: Recall domain - rule for rational functions

The denominator of a rational function cannot be zero. For the function $f(x)=\frac{x + 5}{x-9}$, we set the denominator equal to zero and solve for $x$.

Step2: Solve the equation for non - domain values

Set $x - 9=0$. Solving for $x$ gives $x = 9$.

Step3: Determine the domain

The domain of the function is all real numbers except $x = 9$. In interval notation, this is $(-\infty,9)\cup(9,\infty)$. Since nothing in the given options is correct, the correct choice is "Nothing in this list is correct".

Answer:

Nothing in this list is correct.