Question

Hello! I’ve been trying to figure this question for a while and have no idea to do it :(

Answer 1

The rational function has a little problem with the domain because the result of 1/0 or anything divided by 0 is not defined, therefore, if the denominator is 0 we have a problem. Then what do we do? Simple! We exclude the value of x that makes the denominator equal to 0, in other words, we don't include the zeros of the denominator in the domain.

Therefore let's find the zeros of the denominator so we can exclude them from the domain!

`\begin{gathered} x^2-196=0 \\ \\ x^2=196 \\ \\ x=\pm√(196) \\ \\ x=\pm14 \end{gathered}`

We have two values of x where the denominator are 0, x = 14 and x = -14. Therefore we must remove that two numbers from the domain of the function.

If the domain were all the real numbers:

`\mathbb{R}`

Now the domain is

`\mathbb{R}-\{-14,14\}`

We can also write it as

`(-\infty,-14)\cup(-14,14)\cup(14,+\infty)`