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

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Answer 1 · 2017-03-13T02:45:03

$x!=5,-3$

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).

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