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:

`(x+7)/(x^2-11x+24)=(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.