Math Questions.... beasue i have no idea what to do..?

Question

ok heres the thing i have like 70 or so problems to do and i am STUCK on these. I have no idea where to start. SOMEONE HELP. and PLEASE for the love of ge SHOW YOUR WORK. SO i can pass my test. lol

find the domains...

f(x) =
1
_____

x-4


f(x)=

5x+1
__________

x^2-3x


f(x)=

2x^2-4x-2
_____________

x^2+2x-3

ok so i would think from you example...

2x^2-4x-2 / x^2+2x-3
i think i would factor
(x+3)(x-1)
x=-3 and x=1

so

(-INFINITY,-3) (-3,1) (1,INFINITY)

????

am i close?

Answer 1

f(x) = 1/ (x - 4)

To find the domain, all you have to do is state what x CAN be. In the case of rational functions, the only requirement is that the denominator is not equal to 0, so the best way to solve for the domain is to EQUATE the denominator to 0, and realize your solution would not include that.

In this case, if x - 4 = 0, then x = 4. Therefore, the domain would be
{x | x is not equal to 4, for real number x}.

In interval notation, it would be (-infinity, 4) U (4, infinity)

The round bracket means "up to but not including 4", and infinity ALWAYS has a round bracket.

2. f(x) = (5x + 1) / (x^2 - 3x)

Again, to find the domain, equate the denominator to 0

x^2 - 3x = 0
x(x - 3) = 0
Therefore, x = {0, 3}

That means your domain will be all numbers excluding 0 and 3.
The domain would be (-infinity, 0) U (0, 3) U (3, infinity)

I want you to do #3 on your own.

Answer 2

1) any real number except 4
2) any real number except 0 and 3
3) any real number except -3 and 1

The domain is the set of all possible values of x that will give the function a real value. As with fractions, it is a mortal sin to divide with 0. What we have done here, is just making sure that the denominator will not be equal to 0 when evaluating an x value. So to solve for it just equate the whole denominator to 0 and solve for the values of x that will make it 0. Then that will be the values that shouldn't be part of the domain. Then any real number except those will give a solution. =)

Answer 3

domains mean the x's, so...

from the top down,

1=x-4
+4 +4
x=5

1=5x+1
-1 -1
0=5x
x=0

plug in numbers to equation
x=0,3

2x^2-4x-2
use quadratic formula
x=(4+/-sqrt(-4^2-4(2)(-2))/2(2)
x=(4+/-sqrt(16+16))/4
x=(4+(4*sqrt(2))/4, (4-(4*sqrt(2))/4

x^2+2x-3
(x+3)(x-1)
x=-3,1


hope this helps!