SOLUTION: a recent homework example said fine the domain of the function: g(x) = x/ (over) x^2 + 9x +14 Want us to find any values of x that are meaningless, specifically,

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Question 180022: a recent homework example said fine the domain of the function:

g(x) = x/ (over) x^2 + 9x +14
Want us to find any values of x that are meaningless, specifically, that would make the denominator = 0. to do this make the denominator = 0
So, x^2 +9x+14 = 0
to show the way to solve it, they now show (x+2)(x+7)=0
Therefore, X= -2, -7
How do you get (x+2)(x+7) = 0 from x^2+9x+14+0?????? What happened here? And where did the '9x' go ??? I am totally confused in how they worked out that -2 and -7 are meaningless. how did they get to this?
Answer by solver91311(24713) About Me  (Show Source):
You can put this solution on YOUR website!


"Meaningless" is really a misleading term in this context. What you want to find are values of the variable that make the function undefined. Any rational function is undefined for values of the variable that make a denominator equal zero.

So, we need to find values of x that satisfy

If you have two binomial factors such as you multiply them by using FOIL (First, Outside, Inside, Last), so:

First: x * x = x^2

Outside x * 2 = 2x

Inside 1 * x = x

Last 1 * 2 = 2

Putting them all together:

In order to solve , you need to work the FOIL process in reverse.

The trick is to find two numbers that multiplied together yield the constant term and when added together give the coefficient on the 1st degree term.

For the given equation, those numbers are 2 and 7. 2 times 7 is 14 and 2 plus 7 is 9. So:

. Let's repeat the FOIL process to verify this is true.

First: x^2 Outside: +7x Inside: +2x Last: +14, so

Now that we are assured that , we can write:



Now we apply the Zero Product Rule. The Zero Product Rule says that if and only if or . Applying this to our problem:

if and only if or

means

means

Let's check this result by substituting these values into the equation we started with:

, so -2 works.

, so -7 works.

So, whenever or , then the denominator of is equal to zero and the function is undefined.

Using set builder notation, you would describe the domain of g thus:



John