Question

Can someone please help me with this math question?
Please? I will fan and give a medal!!

Answer 1

please help me find the domain of
x^2+5x+4
----------
x^2+7x+6

Answer 2

Is this a fraction?

Answer 3

Do you know what domain is?

Answer 4

Can you define domain?

Answer 5

@abbycross167

Answer 6

So domain is all of the numbers that x can be

Answer 7

You can't have the bottom of a fraction (which I'm assuming that is) be 0

Answer 8

I'm sorry I didn't reply soon!! My laptop is very very slow

Answer 9

No problem, @anthonyym posed a very good question. Do you know the question is asking you when it asks for the domain of a function?

Answer 10

yes ma'am/sir but I'm not too sure how to do it... my lesson didn't go over this much

Answer 11

Hint: it's acceptable to state the domain is all values of x excpet (...).
For example,

Answer 12

excpet 0 right?

Answer 13

So the domain of the function is where it "exists".
I know it sounds kinda weird, but think about what you have here, you have a fraction.
There's a rule we learned about fractions a few years ago regarding the number zero, do you remember what it was?

Answer 14

no sir/ma'am

Answer 15

You cant ever divide by zero.
This is the key statement you want to remember when finding the domain of a fraction.
Anytime the denominator is zero THE FUNCTION DOES NOT EXIST, so in this question, when its asking you to find the domain its asking you, where does the denominator not equal zero? Because everywhere its not zero it exists, only when it is zero does it not exist.

So thats the theory behind it, now all we need to do is find the values of x that make the denominator zero!


So we set the denominator equal to zero and solve for x
X^2+7x+6=0
We can factor here
(x+6)(x+1)=0
x=-6
x=-1
So when x=-6 and when x=-1 the function does not exist, because it make the denominator equal to zero, and we cant divide by zero.
Therefore, you can write this as:
\[D: (-\infty,-6) U (-6, -1)U(-1, \infty)\]

Answer 16

@legomyego180 I'm not sure what this is - D:(−∞,−6)U(−6,−1)U(−1,∞) ?

Answer 17

It's called "interval notation" and its the formal way of expressing the domain of a function.
So lets break it down
First off the D just means Domain
D:(−∞,−6)U(−6,−1)U(−1,∞)

The parentheses and numbers inside show where the function EXISTS.
So the first set of parenthees say this function exists everywhere between negative infinity and -6.

In interval notation you can use parentheses and you can use brackets, but each means something different:
When you use a bracket it means the x value goes up to exactly that number.
For example [1,4] would mean the function exists from the x values of exactly 1.0 to exactly 4.0.
Now the parentheses are little trickier, and you will learn more about this idea if you progress into upper mathematics classes.
Remember in our solution earlier we said that our function existed everywhere except where x was exactly equal to -6 and -1. Lets draw a number line to visualize this.

Answer 18

\[x^2+7x+6 \neq0\]
\[x^2+6x+x+6 \neq 0\]
\[x \left( x+6 \right)+1\left( x+6 \right)\neq 0\]
\[\left( x+6 \right)(x+1) \neq0\]
Domain is \[R-\left( -6,-1 \right)\]