anonymous
  • anonymous
Help with these Pre-Calc questions!?!
Mathematics
  • Stacey Warren - Expert brainly.com
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SOLVED
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chestercat
  • chestercat
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anonymous
  • anonymous
Determine the domain of the function: |dw:1378325376083:dw|
anonymous
  • anonymous
@jim_thompson5910 @phi
jdoe0001
  • jdoe0001
for a rational, the domain has the constraint in the denominator the fraction MUST NOT be UNDEFINED, and thus that only happens when the denominator is 0 so if the denominator has any variables, they mustn't take any values that will make the denominator 0 so in \(\bf x(x^2-81)\) <--- what values for "x" make THAT zero?

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phi
  • phi
The domain is all real numbers, *EXCEPT* for when x = a number that causes you to divide by 0
anonymous
  • anonymous
These are my answers.
phi
  • phi
as jdoe shows, you have to solve x(x-9)(x+9) = 0 for all the "bad" x's
phi
  • phi
you should learn to trick to how to solve x(x-9)(x+9) = 0 notice that if x is 0, you will get 0* (0-9)* (0+9) and that will be 0 (because when you multiply by 0, you will get 0) if (x-9) is zero, you will end up with 0 if (x+9 is zero, you will get zero. so the problem becomes 3 problems. Solve x=0 x-9=0 x+9 =0 Obviously the first equation is *very* easy. It is already solved. It says when x=0 , the bottom will be 0, and you will divide by 0, and that is NOT allowed. can you find the other 2 "bad" values for x that you are not allowed to use ?
anonymous
  • anonymous
I'm thinking it would be either B or D in my answer list @phi
phi
  • phi
before choosing an answer, can you answer the question can you find the "bad" values for x that you are not allowed to use ? Solve x=0 x-9=0 x+9 =0
phi
  • phi
what value of x makes x-9=0 true ?
phi
  • phi
if you know algebra you would add +9 to both sides x -9 + 9 = 0 +9 and simplify
anonymous
  • anonymous
oh okay so i'm not sure what the "bad" values would be..
anonymous
  • anonymous
wouldn't everything equal to 0?
phi
  • phi
Do you know how to figure out h(0) ? h(0) means replace x with 0 in the expression everywhere you see x, erase it, and put a 0 in its place. For example \[ h(0) = \frac{0 \cdot 8}{0 \cdot (0^2-81)} \] can you simplify the top and bottom ?
phi
  • phi
the top is 0*8= 0. that is ok the bottom is 0 times (0*0-81) the 0*0-81 is -81 and 0 times -81 is 0 the bottom is 0 You are not allowed to divide by 0. So we make a note: x is not allowed to be 0 (It is a "bad" x". we say x≠0
phi
  • phi
so if x=0 was the only bad x, we would say the domain (the good x's) is { x | x≠0 } which is geek speak for x can be any number except x is not 0
phi
  • phi
However, in your problem there are other "bad" x's that make the bottom 0. we have to find them, as list them as not allowed.
anonymous
  • anonymous
okay. is there a fast way to get to my answer? I still have more questions too..
phi
  • phi
so your first job is to find the bad x's that would make the bottom zero. You could test your choices, for example choice (a) says x≠ 9 and x≠ -9 you could see what happens to the bottom if x=9. if you get a zero, you know x≠9
phi
  • phi
If you understand how to solve x(x-9)(x+9) = 0 to find the answers: x=0, x= 9, x=-9 as the answers then know how to write the domain as { x | x≠ bad values} you could answer this quickly.
anonymous
  • anonymous
ok well since it can't equal 0 then my answer would either be B or D right? How do i determine which is correct?
anonymous
  • anonymous
@phi
phi
  • phi
if x is 9 what is (x^2 - 81) ?
anonymous
  • anonymous
0
phi
  • phi
if x is -9 what is (x^2 - 81) ?
anonymous
  • anonymous
0
phi
  • phi
-9*-9 - 81 = 81 - 81 =0 the 3 x values that you need to exclude are x=0, x=±9 which choice excludes those values ?
anonymous
  • anonymous
so it would be C?
phi
  • phi
which choice shows x is not allowed to be 0, 9 or -9 ? the domain is written as { x | x≠ bad values}
anonymous
  • anonymous
D shows that
phi
  • phi
This would be much easier if you learn as you go. It is much harder to answer these questions if you have not learned the material.
anonymous
  • anonymous
was i right? is D the answer?
phi
  • phi
yes

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