anonymous
  • anonymous
find the domain for y=-2/3x+6 answer must be expressed in set notation. how do i do this please?
Mathematics
  • Stacey Warren - Expert brainly.com
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SOLVED
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schrodinger
  • schrodinger
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dape
  • dape
Is it \[ y=-\frac{2}{3x+6}?\]
dape
  • dape
Or is it \[ y=-\frac{2}{3x}+6? \]
anonymous
  • anonymous
the second one

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dape
  • dape
Okay, can you figure out any value of \(x\) that won't work in the forumla?
anonymous
  • anonymous
i divided the right side by -2/3, which gave me -4
dape
  • dape
You shouldn't need to do anything to this formula to find the domain.
dape
  • dape
The thing is that if you try to put \(x=0\) into the formula, you get division by 0, which is undefined and so \(x=0\) can not be in the domain.
dape
  • dape
The domain is basically all values of \(x\) which you can put into the formula so it makes sense.
dape
  • dape
Now, all other values of \(x\) work except 0. Do you know set notation?
anonymous
  • anonymous
no
dape
  • dape
You could write "x is some real number except zero" in set notation as \(x\in\mathbb{R}\setminus\{0\}\) so if we call the domain \(D\) we have, in set-builder notation \(D=\{x\ |\ x\in\mathbb{R}\setminus\{0\}\}\). This reads "the domain is equal to the set of x's such that x is some real number except zero". The bar reads "such that". We could also write \(D=\{x\in\mathbb{R}\ |\ x\neq0\}\), this is a better/cleaner way, it reads "the domain is equal to the set of real x's such that x is not zero".
anonymous
  • anonymous
ok thank you

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