Question

What's the domain of `g(x)=(x^2-5x+4)/(x^2-2x-15)`?

Answer 1

`x!=5,-3`

Explanation:

We have the function:

`g(x)=(x^2-5x+4)/(x^2-2x-15)`

Let's first talk about the values of `x` that won't be allowed in the domain. Why would an `x` value be disallowed?

In this case, when dealing with a fraction, we can't have the denominator be 0. So what values of `x` will make the denominator 0?

We can find that by saying:

`x^2-2x-15=0`

and now solving for `x`:

`(x-5)(x+3)=0`

`x=5, -3`

And so these are the two values that aren't allowed.

We can see that in the graph:

graph{(x^2-5x+4)/(x^2-2x-15) [-33.28, 39.8, -13.83, 22.75]}

(If you scroll on the graph, you can zoom in on those two `x` values to see they are disallowed).