Question

Please help! Thanks!

what is the domain for the following function?
y=
`(2x)/(x-3)`

A.) {x ≠ -3}
B.) {all real numbers}
C.) {x ≠ 3}
D.) {x ≠ 0}

Answer 1

C. All real numbers except x=3.

Explanation:

Domain is all the numbers that you can plug in and the expression will exist for that number you plugged in.

The given expression is a fraction. In a fraction, we have to worry about dividing by 0.

x-3 is 0 when x=0+3=3 (added 3 on both sides).

So the domain is all real numbers except x=3.

The reason we do not want to allow x to be 3 is because you will get:

`(2(3))/(3-3)=(6)/(0)` which is not defined.