Find the domain of each function

G(x)= 2/ x^2 + x - 12

That's division. 2 over the other stuff

domain are the valid inputs to your function. easiest way to determine that is to determine what inputs are not valid. so when is that function not valid? when the denominator is 0. so set the denominator to 0. domain is every x that doesn't make it 0.

in that case any x but zero is valid?

it makes sense what you said but how do i go about figuring out which ones will be invalid without plugging in an infinite amount of numbers to see if they are valid? that one seems easier to see but im sure theyll get harder

no, when the bottom is equal to 0

bottom encompass the whole " x^2 + x - 12"

so set that =0 and solve

This post was edited by saber_x3 on Jan 21 2014 11:07pm

so 2/ x^2 + x -12 = 0

x^2 (square root) + x = 12 (sqaure root)

x + x = 3.464....

2x= 3.464...

x = 1.732

2/1.732 = 1.1547....


is this right ?

No. Take a look at what you just did. we'll apply the logic to some simple numbers to make it easier for you to see what's wrong

1^2 + 1 = 2
1^2 (sqrt this) + 1 = 2 (sqrt this)
1 + 1 = 1.41
2 = 1.41

does that sound right?

/edit: you can also just put your x back into the original problem. if it's not in the domain, you won't be able to.

This post was edited by carteblanche on Jan 21 2014 11:36pm

No

I absolutely hate math.

it's an equation. that means both sides are equal. if you square root the entire right side, you have to square root the entire left side.

But to speed things up, i'll go ahead and tell you that you have to factor it. or if you can't figure out how to factor it, use the quadratic formula.

quick factoring tips:
x^2 + ax + b = 0

find the factors of b that add to get a
step 1) get the factors of b
step 2) for each one, add them up. do any of them get a?

This post was edited by carteblanche on Jan 21 2014 11:39pm

so 2/ x^2 + x -12 = 0

how can i factor x^2? everything would just be 2x?

(x)(x)

2 / 2x + 2x + 2x + 2x + x -12 = 0

2/ 9x-12=0

+12

2/ 9x=12

2/ 1.333333333333

= 1.5 ish


yes?

take a look at your very first step:
2/( x^2 + x -12) = 0

this implies G(x) = 0
but if G(x) = 0, then G(x) exists for that value of x. if it exists, then it's in the domain. so you're already off to the wrong start. you need to find when G(x) does NOT exist.

and as for factoring:
x^2 + x -12 = 0
a = 1
b = -12
find factors of b that add to get a