Question

find the domain for y=-2/3x+6 answer must be expressed in set notation. how do i do this please?

Answer 1

Is it
\[ y=-\frac{2}{3x+6}?\]

Answer 2

Or is it
\[ y=-\frac{2}{3x}+6? \]

Answer 3

the second one

Answer 4

Okay, can you figure out any value of \(x\) that won't work in the forumla?

Answer 5

i divided the right side by -2/3, which gave me -4

Answer 6

You shouldn't need to do anything to this formula to find the domain.

Answer 7

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.

Answer 8

The domain is basically all values of \(x\) which you can put into the formula so it makes sense.

Answer 9

Now, all other values of \(x\) work except 0. Do you know set notation?

Answer 10

no

Answer 11

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".

Answer 12

ok thank you