Question

Find all values of x that are not in the domain of g. If there is more than one value, separate them with commas.

Answer 1

Given the function:

`g(x)=(x+1)/(x^2-2x-8)`

Let's find all the values of x that are not in the domain of the given function.

The domain of a function is all possible values of x which makes the function defined.

For the given rational function to be defined, the denominator must not tend to zero.

To find the domain, let's equate the denominator to zero and solve for x.

We have:

`x^2-2x-8=0`

Now, factor the expression by the left using the AC method.

Find a pair of numbers whose sum is -2 and whose product is -8.

We have:

-4 and 2

Hence, we have the factors:

`(x-4)(x+2)=0`

Equate each factor to zero and solve for x:

`\begin{gathered} x-4=0 \\ \text{Add 4 to both sides:} \\ x-4+4=0+4 \\ x=4 \\ \\ \\ x+2=0 \\ \text{Subtract 2 from both sides:} \\ x+2-2=0-2 \\ x=-2 \end{gathered}`

Therefore, the values of x that are not in the domain are: -2, 4.

ANSWER:

x = -2, 4