Question

find the domain of the function defined in the picture .state answer in interval form.

Answer 1

We will determine the domain of the function as follows:

$\frac{x+7}{x^2-11x+24}=\frac{x+7}{(x-3)(x-8)}$

So, the domain is the following:

$D=\mleft(-\infty,3\mright)\wedge(3,8)\wedge(8,\infty)$

**Explanation***

In order to determine the domain of the function, we factor the denominator and evaluate at which points the denominator will become zero. [When this happens the function is not defined and thus those values do not belong in the domain].

When we factor the denominator, we obtain:

$x^2-11x+24=(x-3)(x-8)$

So, we equal the factor to zero and find which points do not belong in the domain:

$(x-3)(x-8)=0\Rightarrow\begin{cases}x=3 \\ x=8\end{cases}$

So, the equation "makes sense" in all of the real numbers, except when x = 3 and x = 8.